def exchange(hand,receive):
    if(hand[0]%2==1):
        hand[0]-=1
    hand[0]/=2
    receive[0]+=hand[0]

A=[0]
B=[0]
A[0],B[0],K=map(int,input().split())

for i in range(K):
    if(i%2==0):
        exchange(A,B)
    else:
        exchange(B,A)

print("{} {}".format(int(A[0]),int(B[0])))

Score : 200 points

Problem Statement

In the beginning, Takahashi has A cookies, and Aoki has B cookies.
They will perform the following operation alternately, starting from Takahashi:

If the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person.

Find the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total.

Constraints

1 \leq A,B \leq 10^9

1 \leq K \leq 100

A,B and K are integers.

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total.

Sample Input 1

5 4 2

Sample Output 1

5 3

The process will go as follows:

In the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively.

Takahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively.

Aoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively.

Sample Input 2

3 3 3

Sample Output 2

1 3

Sample Input 3

314159265 358979323 84

Sample Output 3

448759046 224379523


N = int(input())
if N == 1:
  print('Yes')
  print(2)
  print(1, 1)
  print(1, 1)
  quit()

S = [{1, 2}, {1, 3}, {2, 3}]
n = 3
while n < N:
  l = len(S)
  s = set()
  for i in range(l):
    n += 1
    S[i].add(n)
    s.add(n)
  S.append(s)

if n == N:
  print('Yes')
  print(len(S))
  for s in S:
    print(len(s), *s)
else:
  print('No')

Global OOD problem IDs are disjoint from train, validation, and in-distribution test problem IDs.

Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Submitted source-code file size, in bytes.

Execution CPU time reported by official Project CodeNet metadata, in milliseconds.

Peak memory usage reported by official Project CodeNet metadata, in kilobytes.


n = int(input())

if n == 1:
    print("Hello Wrold")
    exit()
else:
    a = int(input())
    b = int(input())
    print(a+b)

Score: 100 points

Problem Statement

In 2020, AtCoder Inc. with an annual sales of more than one billion yen (the currency of Japan) has started a business in programming education.

One day, there was an exam where a one-year-old child must write a program that prints Hello World, and a two-year-old child must write a program that receives integers A, B and prints A+B.

Takahashi, who is taking this exam, suddenly forgets his age.

He decides to write a program that first receives his age N (1 or 2) as input, then prints Hello World if N=1, and additionally receives integers A, B and prints A+B if N=2.

Write this program for him.

Constraints

N is 1 or 2.

A is an integer between 1 and 9 (inclusive).

B is an integer between 1 and 9 (inclusive).

Input

Input is given from Standard Input in one of the following formats:

1

2
A
B

Output

If N=1, print Hello World; if N=2, print A+B.

Sample Input 1

1

Sample Output 1

Hello World

As N=1, Takahashi is one year old. Thus, we should print Hello World.

Sample Input 2

2
3
5

Sample Output 2

8

As N=2, Takahashi is two years old. Thus, we should print A+B, which is 8 since A=3 and B=5.


n, m = map(int, input().split())
values = []

def pfac(n):
    values = [1, n]
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            values.append(i)
            values.append(n // i)
    return values

for i in pfac(m):
    if m % i == 0 and m / i >= n:
        values.append(i)
print(max(values))

Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000


input_line = str(input())
s = []

for i in range(len(input_line)):
    if input_line[i] == '9':
        s.append('1')
    elif input_line[i] == '1':
        s.append('9')
    else:
        s.append(input_line[i])

print(s)

mojiretu = ''

for x in s:
    mojiretu += x

print(mojiretu)

Score : 100 points

Problem Statement

Cat Snuke is learning to write characters.
Today, he practiced writing digits 1 and 9, but he did it the other way around.

You are given a three-digit integer n written by Snuke.
Print the integer obtained by replacing each digit 1 with 9 and each digit 9 with 1 in n.

Constraints

111 \leq n \leq 999

n is an integer consisting of digits 1 and 9.

Input

Input is given from Standard Input in the following format:

n

Output

Print the integer obtained by replacing each occurrence of 1 with 9 and each occurrence of 9 with 1 in n.

Sample Input 1

119

Sample Output 1

991

Replace the 9 in the ones place with 1, the 1 in the tens place with 9 and the 1 in the hundreds place with 9. The answer is 991.

Sample Input 2

999

Sample Output 2

111


for c in list(input()):
	if c == "9":
		c = "1"
	elif c == "1":
		c = "9"
	print(c, end="")
print("")


a,b,c = list(map(int, list(str(input()))))
if not (a == b and b == c):
    if (b >= a and c >= a) or (b == a and c >= a):
        a += 1
    b = a; c = a

ans = list(map(str, [a,b,c]))
print("".join(ans))

Score : 200 points

Problem Statement

Kurohashi has never participated in AtCoder Beginner Contest (ABC).

The next ABC to be held is ABC N (the N-th ABC ever held).
Kurohashi wants to make his debut in some ABC x such that all the digits of x in base ten are the same.

What is the earliest ABC where Kurohashi can make his debut?

Constraints

100 \leq N \leq 999

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If the earliest ABC where Kurohashi can make his debut is ABC n, print n.

Sample Input 1

111

Sample Output 1

111

The next ABC to be held is ABC 111, where Kurohashi can make his debut.

Sample Input 2

112

Sample Output 2

222

The next ABC to be held is ABC 112, which means Kurohashi can no longer participate in ABC 111.
Among the ABCs where Kurohashi can make his debut, the earliest one is ABC 222.

Sample Input 3

750

Sample Output 3

777


N = int(input())
l = list(map(int, input().split()))

odd = {}
even = {}
for i in range(N):
    tmp = l[i]
    if i % 2:
        if not odd.get(tmp):
            odd[tmp] = 0
        odd[tmp] += 1
    else:
        if not even.get(tmp):
            even[tmp] = 0
        even[tmp] += 1

odd_max = sorted(odd.items(), key=lambda x: -x[1])[0][0]
even_max = sorted(even.items(), key=lambda x: -x[1])[0][0]

odd_switch = sum([v for k, v in odd.items() if k != odd_max])
even_switch = sum([v for k, v in even.items() if k != even_max])

if odd_switch + even_switch == 0:
    print(N // 2)
else:
    print(odd_switch + even_switch)

Score : 300 points

Problem Statement

A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:

For each i = 1,2,..., n-2, a_i = a_{i+2}.

Exactly two different numbers appear in the sequence.

You are given a sequence v_1,v_2,...,v_n whose length is even.
We would like to make this sequence /\/\/\/ by replacing some of its elements.
Find the minimum number of elements that needs to be replaced.

Constraints

2 \leq n \leq 10^5

n is even.

1 \leq v_i \leq 10^5

v_i is an integer.

Input

Input is given from Standard Input in the following format:

n
v_1 v_2 ... v_n

Output

Print the minimum number of elements that needs to be replaced.

Sample Input 1

4
3 1 3 2

Sample Output 1

1

The sequence 3,1,3,2 is not /\/\/\/, but we can make it /\/\/\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.

Sample Input 2

6
105 119 105 119 105 119

Sample Output 2

0

The sequence 105,119,105,119,105,119 is /\/\/\/.

Sample Input 3

4
1 1 1 1

Sample Output 3

2

The elements of the sequence 1,1,1,1 are all the same, so it is not /\/\/\/.


def GetMaxes(d):
    m = []
    for k, v in d.items():
        m.append([k,v])
    m.sort(key=lambda x:-x[1])

    if len(m) == 1:
        m.append([0, 0])
    return m[:2]

def main():
    n = int(input())
    v = list(map(int, input().split()))

    dic0 = dict()
    dic1 = dict()
    d = [dic0, dic1]
    for i in range(n):
        dic = d[i%2]
        if v[i] not in dic:
            dic[v[i]] = 1
        else:
            dic[v[i]] += 1

    m0 = GetMaxes(d[0])
    m1 = GetMaxes(d[1])

    if m0[0][0] == m1[0][0]:
        take0 = m0[0][1] + m1[1][1]
        take1 = m1[0][1] + m0[1][1]
        if take0 > take1:
            print(n-take0)
        else:
            print(n-take1)
    else:
        print(n - m0[0][1] - m1[0][1])

if __name__ == "__main__":
    main()


N = int(input())
V =  [int(i) for i in input().split()]
V1 = [V[2*j-2] for j in range(1, N//2+1)]
V2 = [V[2*j-1] for j in range(1, N//2+1)]
#print(V1, V2)

def dict(x):
  D = {}
  for i in x:
    if i in D:
      D[i] += 1
    else:
      D.setdefault(i, 1)
  return D

dictV1 = dict(V1)
dictV2 = dict(V2)
#print(dictV1, dictV2)

sortdictV1 = sorted(dictV1.items(), key=lambda x:x[1], reverse=True)
sortdictV2 = sorted(dictV2.items(), key=lambda x:x[1], reverse=True)
a = 0
if sortdictV1[0][0] != sortdictV2[0][0]:
    a = N - sortdictV1[0][1] - sortdictV2[0][1]
else:
  if len(dictV1) == len(dictV2) == 1:
    a = N // 2
  else:
    if len(dictV1) == 1:
      a = N - sortdictV1[0][1] - sortdictV2[1][1]
    elif len(dictV2) == 1:
      a = N - sortdictV1[1][1] - sortdictV2[0][1]
    else:
      a = min(N - sortdictV1[0][1] - sortdictV2[1][1], N - sortdictV1[1][1] - sortdictV2[0][1])
print(a)


import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

S = '-' + sr()
N = len(S) - 1
def solve(S):
    if S[1] == '0':
        print(-1)
        exit()
    if S[N] == '1':
        print(-1)
        exit()
    prev = 1
    for n in range(1,N//2 + 1):
        if S[n] != S[N-n]:
            print(-1)
            exit()
        if S[n] == '0':
            continue
        for i in range(prev,n):
            print(i, n)
        prev = n
    for x in range(prev, N):
        print(x, N)

solve(S)

Score : 700 points

Problem Statement

You are given a string s of length n.
Does a tree with n vertices that satisfies the following conditions exist?

The vertices are numbered 1,2,..., n.

The edges are numbered 1,2,..., n-1, and Edge i connects Vertex u_i and v_i.

If the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.

If the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.

If such a tree exists, construct one such tree.

Constraints

2 \leq n \leq 10^5

s is a string of length n consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

s

Output

If a tree with n vertices that satisfies the conditions does not exist, print -1.

If a tree with n vertices that satisfies the conditions exist, print n-1 lines.
The i-th line should contain u_i and v_i with a space in between.
If there are multiple trees that satisfy the conditions, any such tree will be accepted.

Sample Input 1

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.


from collections import Counter

S=input()
T=input()
N=len(S)
d=dict()

for i in range(N):
  if S[i]!=T[i]:
    if T[i] not in d:
      d[T[i]] = set(S[i])
    else:
      d[T[i]].add(S[i])

ans="Yes"
for pair in d:
  if len(d[pair])>1:
    ans="No"
print(ans)

Score : 300 points

Problem Statement

You are given strings S and T consisting of lowercase English letters.

You can perform the following operation on S any number of times:

Operation: Choose two distinct lowercase English letters c_1 and c_2, then replace every occurrence of c_1 with c_2, and every occurrence of c_2 with c_1.

Determine if S and T can be made equal by performing the operation zero or more times.

Constraints

1 \leq |S| \leq 2 \times 10^5

|S| = |T|

S and T consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S
T

Output

If S and T can be made equal, print Yes; otherwise, print No.

Sample Input 1

azzel
apple

Sample Output 1

Yes

azzel can be changed to apple, as follows:

Choose e as c_1 and l as c_2. azzel becomes azzle.

Choose z as c_1 and p as c_2. azzle becomes apple.

Sample Input 2

chokudai
redcoder

Sample Output 2

No

No sequences of operation can change chokudai to redcoder.

Sample Input 3

abcdefghijklmnopqrstuvwxyz
ibyhqfrekavclxjstdwgpzmonu

Sample Output 3

Yes


from math import factorial

nm = input().split()
n = int(nm[0])
m = int(nm[1])

f = []

i = 2
j = 0
while (m > 1) and i<=m:
    while m%i == 0:
        m /= i
        j += 1
    if j >= 1:
        f.append(j)
    i += 1
    j = 0

ans = 1

for k in f:
    if k > 0:
        ans *= factorial(n+k-1) // (factorial(k) * factorial(n-1))

print(int(ans) % (10**9+7))

Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001


import sys
input = sys.stdin.readline

N, X = map(int, input().split())
L = [int(v) for v in input().split()]
L.sort()

ans = 0
for i in range(N):
    a = L[i]

    if X >= a:
        X -= a
        ans += 1

if ans == N and X > 0:
    ans -= 1

print(ans)

Score : 200 points

Problem Statement

There are N children, numbered 1, 2, ..., N.

Snuke has decided to distribute x sweets among them.
He needs to give out all the x sweets, but some of the children may get zero sweets.

For each i (1 \leq i \leq N), Child i will be happy if he/she gets exactly a_i sweets.
Snuke is trying to maximize the number of happy children by optimally distributing the sweets.
Find the maximum possible number of happy children.

Constraints

All values in input are integers.

2 \leq N \leq 100

1 \leq x \leq 10^9

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Print the maximum possible number of happy children.

Sample Input 1

3 70
20 30 10

Sample Output 1

2

One optimal way to distribute sweets is (20, 30, 20).

Sample Input 2

3 10
20 30 10

Sample Output 2

1

The optimal way to distribute sweets is (0, 0, 10).

Sample Input 3

4 1111
1 10 100 1000

Sample Output 3

4

The optimal way to distribute sweets is (1, 10, 100, 1000).

Sample Input 4

2 10
20 20

Sample Output 4

0

No children will be happy, no matter how the sweets are distributed.


n, x = map(int, input( ).split())
a = list(map(int, input().split()))
counter = 0
for i in sorted(a):
  x -= i
  counter += 1
  if x<0:
    print(counter-1)
  elif x==0:
    print(counter)
  else:
    if counter==n:
      print(counter-1)


import math
N, X=map(int, input().split())
x=[]
x=list(map(int, input().split()))
A=0
B=0
C=(N+1)*X
d=math.ceil(N/2)
for i in range(N-2):
    A+=(N-2-i)*2*x[i]
for j in range(N):
    C+=x[j]*5
if X*(d-1)<=A:
    B=C+X*(d-1)
else:
    B=C+A
print(B)

Score : 700 points

Problem Statement

Snuke has decided to use a robot to clean his room.

There are N pieces of trash on a number line.
The i-th piece from the left is at position x_i.
We would like to put all of them in a trash bin at position 0.

For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.

The robot is initially at position 0.
It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.

The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.)
Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.

Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.

Constraints

1 \leq N \leq 2 \times 10^{5}

0 < x_1 < ... < x_N \leq 10^9

1 \leq X \leq 10^9

All values in input are integers.

Partial Scores

400 points will be awarded for passing the test set satisfying N \leq 2000.

Input

Input is given from Standard Input in the following format:

N X
x_1 x_2 ... x_{N}

Output

Print the answer.

Sample Input 1

2 100
1 10

Sample Output 1

355

Travel to position 10 by consuming 10 points of energy.

Pick up the piece of trash by consuming 100 points of energy.

Travel to position 1 by consuming 36 points of energy.

Pick up the piece of trash by consuming 100 points of energy.

Travel to position 0 by consuming 9 points of energy.

Put the two pieces of trash in the trash bin by consuming 100 points of energy.

This strategy consumes a total of 10+100+36+100+9+100=355 points of energy.

Sample Input 2

5 1
1 999999997 999999998 999999999 1000000000

Sample Output 2

19999999983

Sample Input 3

10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746

Sample Output 3

150710136

Sample Input 4

16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408

Sample Output 4

3256017715


def is_even(num):
    if num == 0:
        return True
    return num % 2 == 0

height, width = list(map(int, input().split()))
coin_table = [list(map(is_even, map(int, input().split()))) for i in range(height)]

move_list = list()

for h in range(height):
    for w in range(width):
        if not(coin_table[h][w]):
            coin_table[h][w] = True
            if w == width-1:
                if h == height-1:
                    break
                coin_table[h + 1][w] = not coin_table[h + 1][w]
                move_list.append([h + 1, w + 1, h + 2, w + 1])
            else:
                coin_table[h][w+1] = not coin_table[h][w+1]
                move_list.append([h + 1, w + 1, h + 1, w + 2])

print(len(move_list))
for i in range(len(move_list)):
    print("{0} {1} {2} {3}".format(move_list[i][0], move_list[i][1], move_list[i][2], move_list[i][3]))

Score : 400 points

Problem Statement

There is a grid of square cells with H horizontal rows and W vertical columns. The cell at the i-th row and the j-th column will be denoted as Cell (i, j).

In Cell (i, j), a_{ij} coins are placed.

You can perform the following operation any number of times:

Operation: Choose a cell that was not chosen before and contains one or more coins, then move one of those coins to a vertically or horizontally adjacent cell.

Maximize the number of cells containing an even number of coins.

Constraints

All values in input are integers.

1 \leq H, W \leq 500

0 \leq a_{ij} \leq 9

Input

Input is given from Standard Input in the following format:

H W
a_{11} a_{12} ... a_{1W}
a_{21} a_{22} ... a_{2W}
:
a_{H1} a_{H2} ... a_{HW}

Output

Print a sequence of operations that maximizes the number of cells containing an even number of coins, in the following format:

N
y_1 x_1 y_1' x_1'
y_2 x_2 y_2' x_2'
:
y_N x_N y_N' x_N'

That is, in the first line, print an integer N between 0 and H \times W (inclusive), representing the number of operations.

In the (i+1)-th line (1 \leq i \leq N), print four integers y_i, x_i, y_i' and x_i' (1 \leq y_i, y_i' \leq H and 1 \leq x_i, x_i' \leq W), representing the i-th operation. These four integers represents the operation of moving one of the coins placed in Cell (y_i, x_i) to a vertically or horizontally adjacent cell, (y_i', x_i').

Note that if the specified operation violates the specification in the problem statement or the output format is invalid, it will result in Wrong Answer.

Sample Input 1

2 3
1 2 3
0 1 1

Sample Output 1

3
2 2 2 3
1 1 1 2
1 3 1 2

Every cell contains an even number of coins after the following sequence of operations:

Move the coin in Cell (2, 2) to Cell (2, 3).

Move the coin in Cell (1, 1) to Cell (1, 2).

Move one of the coins in Cell (1, 3) to Cell (1, 2).

Sample Input 2

3 2
1 0
2 1
1 0

Sample Output 2

3
1 1 1 2
1 2 2 2
3 1 3 2

Sample Input 3

1 5
9 9 9 9 9

Sample Output 3

2
1 1 1 2
1 3 1 4


k=int(input())
if k%2==0:
    print((k//2)**2)
else:
    a=k//2
    print(a*(k-a))

Score : 100 points

Problem Statement

Find the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive). The order does not matter.

Constraints

2\leq K\leq 100

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive).

Sample Input 1

3

Sample Output 1

2

Two pairs can be chosen: (2,1) and (2,3).

Sample Input 2

6

Sample Output 2

9

Sample Input 3

11

Sample Output 3

30

Sample Input 4

50

Sample Output 4

625


n,k = map(int,input().split())
if k%2!=0:
    count = 0
    i = 1
    check = True
    while check:
        if n <= k * i:
            check = False
        else:
            count += 1
            i += 1
    print(count**2*count)
import math
if k%2==0:
    count = 0
    i = 1
    check = True
    while check:
        if n < (k/2) * i:
            check = False
        else:
            count += 1
            i += 1
    ans_1 = math.ceil(count/2)
    ans_2 = math.ceil(count/2)-1
    print(ans_1**2*ans_1+ans_2**2*ans_2)

Score : 300 points

Problem Statement

You are given integers N and K. Find the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.
The order of a,b,c does matter, and some of them can be the same.

Constraints

1 \leq N,K \leq 2\times 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.

Sample Input 1

3 2

Sample Output 1

9

(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.

Sample Input 2

5 3

Sample Output 2

1

Sample Input 3

31415 9265

Sample Output 3

27

Sample Input 4

35897 932

Sample Output 4

114191


n,i =  list(map(int,(input().split())))

print(n-(i-1))

Score : 100 points

Problem Statement

There is an N-car train.

You are given an integer i. Find the value of j such that the following statement is true: "the i-th car from the front of the train is the j-th car from the back."

Constraints

1 \leq N \leq 100

1 \leq i \leq N

Input

Input is given from Standard Input in the following format:

N i

Output

Print the answer.

Sample Input 1

4 2

Sample Output 1

3

The second car from the front of a 4-car train is the third car from the back.

Sample Input 2

1 1

Sample Output 2

1

Sample Input 3

15 11

Sample Output 3

5


# coding: utf-8
# Your code here!
import bisect

N,K=map(int,input().split())
X=list(map(int,input().split()))

zero=bisect.bisect_left(X,0)

ans=10**18
start=max(0,zero-K)
for i in range(start,start+N-K+1):
    temp=X[i:i+K]
    m=min(0,min(temp))
    M=max(0,max(temp))
    ans=min((abs(m)+abs(M)*2),(abs(m)*2+abs(M)),ans)

print(ans)

Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10


a,b = map(int, input().split())
print((a-1)*(b-1))

Score: 100 points

Problem Statement

There is a farm whose length and width are A yard and B yard, respectively. A farmer, John, made a vertical road and a horizontal road inside the farm from one border to another, as shown below: (The gray part represents the roads.)

What is the area of this yard excluding the roads? Find it.

Note

It can be proved that the positions of the roads do not affect the area.

Constraints

A is an integer between 2 and 100 (inclusive).

B is an integer between 2 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

A B

Output

Print the area of this yard excluding the roads (in square yards).

Sample Input 1

2 2

Sample Output 1

1

In this case, the area is 1 square yard.

Sample Input 2

5 7

Sample Output 2

24

In this case, the area is 24 square yards.


A, B = map(int, input().split())

print((A - 1) * (B - 1))


N = int(input())

if N >= 105:
  print(1)
else:
  print(0)

Score: 200 points

Problem Statement

The number 105 is quite special - it is odd but still it has eight divisors.
Now, your task is this: how many odd numbers with exactly eight positive divisors are there between 1 and N (inclusive)?

Constraints

N is an integer between 1 and 200 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print the count.

Sample Input 1

105

Sample Output 1

1

Among the numbers between 1 and 105, the only number that is odd and has exactly eight divisors is 105.

Sample Input 2

7

Sample Output 2

0

1 has one divisor. 3, 5 and 7 are all prime and have two divisors. Thus, there is no number that satisfies the condition.


# -*- coding: utf-8 -*-
"""
Created on Tue Mar 31 02:12:27 2020

@author: liang
"""

n = int(input())
ans = 0
for num in range(1, n+1,2):
    cnt = 0
    for i in range(1,num+1):
        if num % i == 0:
            cnt += 1
    if cnt == 8:
        ans += 1
print(ans)


n = int(input())
ans = 0
for i in range(1,n+1,2):
    count = 0
    for j in range(1,i+1):
        if i%j==0:
            count += 1
    if count == 8:
        ans += 1
print(ans)


def main():
    n = int(input())
    s = 0

    for i in range(1, n + 1, 2):
        if num_factor(i) == 8:
            s += 1
    print(s)

def num_factor(n):
    if n == 1:
        return 1

    s = 2
    i = 2

    while i * i <= n:
        if n % i == 0:
            if i * i != n:
                s += 2
            else:
                s += 1
        i += 1
    return s

main()


s = list(map(int,input()))
j = 1
for i in s:
	if i != 1:
		j = i
		break
print(j)

Score: 300 points

Problem Statement

Mr. Infinity has a string S consisting of digits from 1 to 9. Each time the date changes, this string changes as follows:

Each occurrence of 2 in S is replaced with 22. Similarly, each 3 becomes 333, 4 becomes 4444, 5 becomes 55555, 6 becomes 666666, 7 becomes 7777777, 8 becomes 88888888 and 9 becomes 999999999. 1 remains as 1.

For example, if S is 1324, it becomes 1333224444 the next day, and it becomes 133333333322224444444444444444 the day after next.
You are interested in what the string looks like after 5 \times 10^{15} days. What is the K-th character from the left in the string after 5 \times 10^{15} days?

Constraints

S is a string of length between 1 and 100 (inclusive).

K is an integer between 1 and 10^{18} (inclusive).

The length of the string after 5 \times 10^{15} days is at least K.

Input

Input is given from Standard Input in the following format:

S
K

Output

Print the K-th character from the left in Mr. Infinity's string after 5 \times 10^{15} days.

Sample Input 1

1214
4

Sample Output 1

2

The string S changes as follows:

Now: 1214

After one day: 12214444

After two days: 1222214444444444444444

After three days: 12222222214444444444444444444444444444444444444444444444444444444444444444

The first five characters in the string after 5 \times 10^{15} days is 12222. As K=4, we should print the fourth character, 2.

Sample Input 2

3
157

Sample Output 2

3

The initial string is 3. The string after 5 \times 10^{15} days consists only of 3.

Sample Input 3

299792458
9460730472580800

Sample Output 3

2


S = input()
K = int(input())

k = 1
while k <= K:
    if S[k-1] != "1":
        print(S[k-1])
        break
    k += 1
else:
    print(1)


N,M,Q = map(int,input().split())
trains = []
question = []
for i in range(M):
    trains.append(list(map(int,input().split())))
for j in range(Q):
    question.append(list(map(int,input().split())))
for que in question:
    ans = 0
    for train in trains:
        if train[0]>=que[0] and train[1]<=que[1]:
            ans+=1
    print(ans)

Score: 400 points

Problem Statement

In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east.
A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).
Takahashi the king is interested in the following Q matters:

The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.

Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.

Constraints

N is an integer between 1 and 500 (inclusive).

M is an integer between 1 and 200 \ 000 (inclusive).

Q is an integer between 1 and 100 \ 000 (inclusive).

1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)

1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q

Output

Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.

Sample Input 1

2 3 1
1 1
1 2
2 2
1 2

Sample Output 1

3

As all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.

Sample Input 2

10 3 2
1 5
2 8
7 10
1 7
3 10

Sample Output 2

1
1

The first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.
The second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.

Sample Input 3

10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10

Sample Output 3

7
9
10
6
8
9
6
7
8
10


N,K = map(int,input().split())
if N % K == 0:
    print(0)
else:
    print(1)

Score : 100 points

Problem Statement

Takahashi has decided to distribute N AtCoder Crackers to K users of as evenly as possible.
When all the crackers are distributed, find the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.

Constraints

1 \leq N,K \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.

Sample Input 1

7 3

Sample Output 1

1

When the users receive two, two and three crackers, respectively, the (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user, is 1.

Sample Input 2

100 10

Sample Output 2

0

The crackers can be distributed evenly.

Sample Input 3

1 1

Sample Output 3

0


n, k = list(map(int, input().split()))
if n%k == 0:
    print(0)
else:
    print(1)


N, K = [int(i) for i in input().split()]

if N % K == 0:
    print(0)
else:
    print(1)


N,K=map(int,input().split())
A=[0 for i in range(K)]
for i in range(N):
    A[i%K]+=1
print(max(A)-min(A))


N,M = list(map(int,input().split()))
A = input().split()

count = 0
A = np.array(A,dtype='int64')
B = np.cumsum(A)
C = np.append([0],B)

L = (1 for i in range(N+1) for t in range(N+1) if i<t and (C[t] - C[i])%M==0)
print(len(list(L)))

Score : 400 points

Problem Statement

There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies.

You will take out the candies from some consecutive boxes and distribute them evenly to M children.

Such being the case, find the number of the pairs (l, r) that satisfy the following:

l and r are both integers and satisfy 1 \leq l \leq r \leq N.

A_l + A_{l+1} + ... + A_r is a multiple of M.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

2 \leq M \leq 10^9

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_N

Output

Print the number of the pairs (l, r) that satisfy the conditions.

Note that the number may not fit into a 32-bit integer type.

Sample Input 1

3 2
4 1 5

Sample Output 1

3

The sum A_l + A_{l+1} + ... + A_r for each pair (l, r) is as follows:

Sum for (1, 1): 4

Sum for (1, 2): 5

Sum for (1, 3): 10

Sum for (2, 2): 1

Sum for (2, 3): 6

Sum for (3, 3): 5

Among these, three are multiples of 2.

Sample Input 2

13 17
29 7 5 7 9 51 7 13 8 55 42 9 81

Sample Output 2

6

Sample Input 3

10 400000000
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

25


r = int(input())
if r < 1200:
    print("ABC")
if 1200 <= r < 2800:
    print("ARC")
else:
    print("AGC")

Score : 100 points

Problem Statement

A programming competition site AtCode regularly holds programming contests.

The next contest on AtCode is called ABC, which is rated for contestants with ratings less than 1200.

The contest after the ABC is called ARC, which is rated for contestants with ratings less than 2800.

The contest after the ARC is called AGC, which is rated for all contestants.

Takahashi's rating on AtCode is R. What is the next contest rated for him?

Constraints

0 ≤ R ≤ 4208

R is an integer.

Input

Input is given from Standard Input in the following format:

R

Output

Print the name of the next contest rated for Takahashi (ABC, ARC or AGC).

Sample Input 1

1199

Sample Output 1

ABC

1199 is less than 1200, so ABC will be rated.

Sample Input 2

1200

Sample Output 2

ARC

1200 is not less than 1200 and ABC will be unrated, but it is less than 2800 and ARC will be rated.

Sample Input 3

4208

Sample Output 3

AGC


s = input()

flag = 0

if s[0] !="A":
  flag = 1

count=0
for i in range(2,len(s)-1):
  if s[i]=="C":
    count +=1

if count !=1:
  flag =1

count =0
s_small = s.lower()
for i in range(len(s)):
  if s_small[i] !=s[i]:
    count += 1

if count !=2:
  flag =1

print("AC" if flag ==0 else "WA")

Score : 200 points

Problem Statement

You are given a string S. Each character of S is uppercase or lowercase English letter.
Determine if S satisfies all of the following conditions:

The initial character of S is an uppercase A.

There is exactly one occurrence of C between the third character from the beginning and the second to last character (inclusive).

All letters except the A and C mentioned above are lowercase.

Constraints

4 ≤ |S| ≤ 10 (|S| is the length of the string S.)

Each character of S is uppercase or lowercase English letter.

Input

Input is given from Standard Input in the following format:

S

Output

If S satisfies all of the conditions in the problem statement, print AC; otherwise, print WA.

Sample Input 1

AtCoder

Sample Output 1

AC

The first letter is A, the third letter is C and the remaining letters are all lowercase, so all the conditions are satisfied.

Sample Input 2

ACoder

Sample Output 2

WA

The second letter should not be C.

Sample Input 3

AcycliC

Sample Output 3

WA

The last letter should not be C, either.

Sample Input 4

AtCoCo

Sample Output 4

WA

There should not be two or more occurrences of C.

Sample Input 5

Atcoder

Sample Output 5

WA

The number of C should not be zero, either.


s = input()
count = 0
for i in range(len(s)):
    if i == 0:
        if s[i] != 'A':
            break
    elif i == 1:
        if s[i].islower():
            pass
        else:
            break
    elif i>1 and i < len(s)-1 :
        if s[i]=='C':
            if count == 0:
                count += 1
            else:
                break
        elif s[i].islower():
            pass
        else:
            break
    elif i == len(s) :
        if s[i].islower():
            print("AC")
            exit()
    else:
        break
print("WA")


list1 = list(map(int, input().split()))
list1.sort()
cost= list1[2]-list1[0]
print(cost)

Score : 100 points

Problem Statement

You have three tasks, all of which need to be completed.

First, you can complete any one task at cost 0.

Then, just after completing the i-th task, you can complete the j-th task at cost |A_j - A_i|.

Here, |x| denotes the absolute value of x.

Find the minimum total cost required to complete all the task.

Constraints

All values in input are integers.

1 \leq A_1, A_2, A_3 \leq 100

Input

Input is given from Standard Input in the following format:

A_1 A_2 A_3

Output

Print the minimum total cost required to complete all the task.

Sample Input 1

1 6 3

Sample Output 1

5

When the tasks are completed in the following order, the total cost will be 5, which is the minimum:

Complete the first task at cost 0.

Complete the third task at cost 2.

Complete the second task at cost 3.

Sample Input 2

11 5 5

Sample Output 2

6

Sample Input 3

100 100 100

Sample Output 3

0


a = list(map(int, input().split()))
a.sort()
num1 = a[1]-a[0]
num2 = a[2]-a[1]
print(int(num1)+int(num2))


S = input()
T = input()

t2 = T + T

if set(S) == set(T):
  if t2.count(S) > 0:
    r = 'Yes'
else:
  r = 'No'

print(r)

Score : 200 points

Problem Statement

You are given string S and T consisting of lowercase English letters.

Determine if S equals T after rotation.

That is, determine if S equals T after the following operation is performed some number of times:

Operation: Let S = S_1 S_2 ... S_{|S|}. Change S to S_{|S|} S_1 S_2 ... S_{|S|-1}.

Here, |X| denotes the length of the string X.

Constraints

2 \leq |S| \leq 100

|S| = |T|

S and T consist of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S
T

Output

If S equals T after rotation, print Yes; if it does not, print No.

Sample Input 1

kyoto
tokyo

Sample Output 1

Yes

In the first operation, kyoto becomes okyot.

In the second operation, okyot becomes tokyo.

Sample Input 2

abc
arc

Sample Output 2

No

abc does not equal arc after any number of operations.

Sample Input 3

aaaaaaaaaaaaaaab
aaaaaaaaaaaaaaab

Sample Output 3

Yes


n = int(input())
A = list(map(int, input().split()))
print(sum([a - 1 for a in A]))

Score : 300 points

Problem Statement

You are given N positive integers a_1, a_2, ..., a_N.

For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).

Here, X\ mod\ Y denotes the remainder of the division of X by Y.

Find the maximum value of f.

Constraints

All values in input are integers.

2 \leq N \leq 3000

2 \leq a_i \leq 10^5

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum value of f.

Sample Input 1

3
3 4 6

Sample Output 1

10

f(11) = (11\ mod\ 3) + (11\ mod\ 4) + (11\ mod\ 6) = 10 is the maximum value of f.

Sample Input 2

5
7 46 11 20 11

Sample Output 2

90

Sample Input 3

7
994 518 941 851 647 2 581

Sample Output 3

4527


N = int(input())
A = list(map(int, input().split()))

A1 = [a - 1 for a in A]

print(sum(A1))


import math

n = int(input())
a = list(map(int, input().split()))
a.append("#")
start = 0
end = 0

ans = 0

while a[start] != "#" :
  if a[start] != a[end]:
    x = end - start
    if x % 2 == 0:
      ans += x // 2
    else:
      ans += math.floor(x / 2)

    start = end

  else:
    end += 1

print(ans)

Score : 200 points

Problem Statement

Takahashi lives in another world. There are slimes (creatures) of 10000 colors in this world. Let us call these colors Color 1, 2, ..., 10000.

Takahashi has N slimes, and they are standing in a row from left to right. The color of the i-th slime from the left is a_i.
If two slimes of the same color are adjacent, they will start to combine themselves. Because Takahashi likes smaller slimes, he has decided to change the colors of some of the slimes with his magic.

Takahashi can change the color of one slime to any of the 10000 colors by one spell.
How many spells are required so that no slimes will start to combine themselves?

Constraints

2 \leq N \leq 100

1 \leq a_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of spells required.

Sample Input 1

5
1 1 2 2 2

Sample Output 1

2

For example, if we change the color of the second slime from the left to 4, and the color of the fourth slime to 5, the colors of the slimes will be 1, 4, 2, 5, 2, which satisfy the condition.

Sample Input 2

3
1 2 1

Sample Output 2

0

Although the colors of the first and third slimes are the same, they are not adjacent, so no spell is required.

Sample Input 3

5
1 1 1 1 1

Sample Output 3

2

For example, if we change the colors of the second and fourth slimes from the left to 2, the colors of the slimes will be 1, 2, 1, 2, 1, which satisfy the condition.

Sample Input 4

14
1 2 2 3 3 3 4 4 4 4 1 2 3 4

Sample Output 4

4


a,b=map(int,input().split())
print('+' if a+b==15 else '*' if a*b==15 else 'x')

Score : 100 points

Problem Statement

You are given two integers a and b.
Determine if a+b=15 or a\times b=15 or neither holds.

Note that a+b=15 and a\times b=15 do not hold at the same time.

Constraints

1 \leq a,b \leq 15

All values in input are integers.

Input

Input is given from Standard Input in the following format:

a b

Output

If a+b=15, print +;
if a\times b=15, print *;
if neither holds, print x.

Sample Input 1

4 11

Sample Output 1

+

4+11=15.

Sample Input 2

3 5

Sample Output 2

*

3\times 5=15.

Sample Input 3

1 1

Sample Output 3

x

1+1=2 and 1\times 1=1, neither of which is 15.


n,m,d = map(int,input().split())
print(2*(m-1)*(n-d)/n/n if d > 0 else (m-1)/n)

Score : 300 points

Problem Statement

Let us define the beauty of a sequence (a_1,... ,a_n) as the number of pairs of two adjacent elements in it whose absolute differences are d.
For example, when d=1, the beauty of the sequence (3, 2, 3, 10, 9) is 3.

There are a total of n^m sequences of length m where each element is an integer between 1 and n (inclusive).
Find the beauty of each of these n^m sequences, and print the average of those values.

Constraints

0 \leq d < n \leq 10^9

2 \leq m \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m d

Output

Print the average of the beauties of the sequences of length m where each element is an integer between 1 and n.
The output will be judged correct if the absolute or relative error is at most 10^{-6}.

Sample Input 1

2 3 1

Sample Output 1

1.0000000000

The beauty of (1,1,1) is 0.

The beauty of (1,1,2) is 1.

The beauty of (1,2,1) is 2.

The beauty of (1,2,2) is 1.

The beauty of (2,1,1) is 1.

The beauty of (2,1,2) is 2.

The beauty of (2,2,1) is 1.

The beauty of (2,2,2) is 0.

The answer is the average of these values: (0+1+2+1+1+2+1+0)/8=1.

Sample Input 2

1000000000 180707 0

Sample Output 2

0.0001807060


N = int(input())
A = list(map(int, input().split()))
ans = 0
for i in range(N):
  for k in range(i+1, N):
    ans = max(ans,abs(A[i] - A[k]))
print(ans)

Score : 200 points

Problem Statement

You are given an integer sequence A of length N.
Find the maximum absolute difference of two elements (with different indices) in A.

Constraints

2 \leq N \leq 100

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum absolute difference of two elements (with different indices) in A.

Sample Input 1

4
1 4 6 3

Sample Output 1

5

The maximum absolute difference of two elements is A_3-A_1=6-1=5.

Sample Input 2

2
1000000000 1

Sample Output 2

999999999

Sample Input 3

5
1 1 1 1 1

Sample Output 3

0


N = int(input())
A = list(map(int, input().split()))
for i in range(N):
  A[i] -= i

mode = sorted(A)[N//2]

ans = 0
for i in range(N):
  ans += abs(A[i]-mode)
print(ans)

Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6


S_original=input('S: ')
S_list=list(S_original)
length_S=len(S_list)

a=0
i=0

while i < length_S:
  if S_list[i]=='+':
    a += 1
    i += 1
  else:
    a = a-1
    i=i+1

print(a)

Score : 100 points

Problem Statement

There is always an integer in Takahashi's mind.

Initially, the integer in Takahashi's mind is 0. Takahashi is now going to eat four symbols, each of which is + or -. When he eats +, the integer in his mind increases by 1; when he eats -, the integer in his mind decreases by 1.

The symbols Takahashi is going to eat are given to you as a string S. The i-th character in S is the i-th symbol for him to eat.

Find the integer in Takahashi's mind after he eats all the symbols.

Constraints

The length of S is 4.

Each character in S is + or -.

Input

Input is given from Standard Input in the following format:

S

Output

Print the integer in Takahashi's mind after he eats all the symbols.

Sample Input 1

+-++

Sample Output 1

2

Initially, the integer in Takahashi's mind is 0.

The first integer for him to eat is +. After eating it, the integer in his mind becomes 1.

The second integer to eat is -. After eating it, the integer in his mind becomes 0.

The third integer to eat is +. After eating it, the integer in his mind becomes 1.

The fourth integer to eat is +. After eating it, the integer in his mind becomes 2.

Thus, the integer in Takahashi's mind after he eats all the symbols is 2.

Sample Input 2

-+--

Sample Output 2

-2

Sample Input 3

----

Sample Output 3

-4


num = 0
s = input()
for op in s:
  if op == '+':
    num += 1
  else:
    num -= 1
print(num)


n, k = map(int, input().split())
a = list(map(int, input().split()))

one = 0
for i in range(n):
    if a[i] == 1:
        one = i + 1
        break

front = -(-(one - 1) // (k - 1))
back = -(-(n - one) // (k - 1))
#print(front, back)
print(front + back)

Score : 300 points

Problem Statement

There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.

On this sequence, Snuke can perform the following operation:

Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.

Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.
Find the minimum number of operations required.
It can be proved that, Under the constraints of this problem, this objective is always achievable.

Constraints

2 \leq K \leq N \leq 100000

A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of operations required.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

One optimal strategy is as follows:

In the first operation, choose the first, second and third elements. The sequence A becomes 1, 1, 1, 4.

In the second operation, choose the second, third and fourth elements. The sequence A becomes 1, 1, 1, 1.

Sample Input 2

3 3
1 2 3

Sample Output 2

1

Sample Input 3

8 3
7 3 1 8 4 6 2 5

Sample Output 3

4


N,K = map(int,input().split())
A = list(map(int,input().split()))
ind = A.index(1)
n = ind//(K-1)
if ind%(K-1):
    n += 1
m = (N-1-ind)//(K-1)
if (N-1-ind)%(K-1):
    m += 1
cmin = n+m
for i in range(max(1,ind+K-N),min(ind,K-1)+1):
    n = (ind-i)//(K-1)
    if (ind-i)%(K-1):
        n += 1
    m = (N-ind-K+i)//(K-1)
    if (N-ind-K+i)%(K-1):
        m += 1
    cnt = n+m+1
    cmin = min(cmin,cnt)
print(cmin)


k = int(input())
r = 0  # 桁数
snuke_list = []

def snuke(num):
    s = 0
    for i in str(num):
        s += int(i)
    return num/s

def snuke_check(num):
    n = str(num)
    keta = len(n)    # numの桁数
    min_snuke = int(n[0] + '9'*(keta-1))
    if snuke(num) <= snuke(min_snuke):
        return True
    else:
        return False

count = 0
while count < 2*k:
    for t in range(1, 150):
        num = int(str(t) + '9' * r)
        if snuke_check(num) is True:
            if num not in snuke_list:
                snuke_list.append(num)
                count += 1
        if count >= 2*k:
            break
    r += 1
snuke_list.sort()
check = []
for n in snuke_list:
    check.append(snuke(n))
for i in range(len(check)):
    if check[i] <= min(check[i:]):
        pass
    else:
        snuke_list[i] = -1

for i in range(k):
    if snuke_list[i] > 0:
        print(snuke_list[i])

Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19


# ABC 100: A – Happy Birthday!
a, b = [int(s) for s in input().split()]
print('Yay!' if a <= 8 and b <= 8 else ':(')

Score: 100 points

Problem Statement

E869120's and square1001's 16-th birthday is coming soon.

Takahashi from AtCoder Kingdom gave them a round cake cut into 16 equal fan-shaped pieces.

E869120 and square1001 were just about to eat A and B of those pieces, respectively,

when they found a note attached to the cake saying that "the same person should not take two adjacent pieces of cake".

Can both of them obey the instruction in the note and take desired numbers of pieces of cake?

Constraints

A and B are integers between 1 and 16 (inclusive).

A+B is at most 16.

Input

Input is given from Standard Input in the following format:

A B

Output

If both E869120 and square1001 can obey the instruction in the note and take desired numbers of pieces of cake, print Yay!; otherwise, print :(.

Sample Input 1

5 4

Sample Output 1

Yay!

Both of them can take desired number of pieces as follows:

Sample Input 2

8 8

Sample Output 2

Yay!

Both of them can take desired number of pieces as follows:

Sample Input 3

11 4

Sample Output 3

:(

In this case, there is no way for them to take desired number of pieces, unfortunately.


#!/usr/bin/env python
# -*- coding: utf-8 -*-

import itertools
import numpy as np

# 入力受け取り
N, M = map(lambda x: int(x), input().split())
cake_scores = [[] for _ in range(N)]
for i in range(N):
    cake_scores[i] = [int(j) for j in input().split()]  # print(score)

cake_id = np.arange(N)  # cakeのID
chosen_cakes_scores = []  # スコアのまとめ
for cake_choice in itertools.combinations(cake_id, M):
    cakes = np.array([cake_scores[i] for i in cake_choice])  # cakes [[スコア], [スコア]...]
    box = np.zeros(len(cakes[0]))  # shape (1, 3)
    for i in cakes:
        box += i
    chosen_cakes_scores.append(np.sum(abs(box)))

print(int(max(chosen_cakes_scores)))

Score: 400 points

Problem Statement

Takahashi became a pastry chef and opened a shop La Confiserie d'ABC to celebrate AtCoder Beginner Contest 100.

The shop sells N kinds of cakes.

Each kind of cake has three parameters "beauty", "tastiness" and "popularity". The i-th kind of cake has the beauty of x_i, the tastiness of y_i and the popularity of z_i.

These values may be zero or negative.

Ringo has decided to have M pieces of cakes here. He will choose the set of cakes as follows:

Do not have two or more pieces of the same kind of cake.

Under the condition above, choose the set of cakes to maximize (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity).

Find the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.

Constraints

N is an integer between 1 and 1 \ 000 (inclusive).

M is an integer between 0 and N (inclusive).

x_i, y_i, z_i \ (1 \leq i \leq N) are integers between -10 \ 000 \ 000 \ 000 and 10 \ 000 \ 000 \ 000 (inclusive).

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1 z_1
x_2 y_2 z_2
: :
x_N y_N z_N

Output

Print the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.

Sample Input 1

5 3
3 1 4
1 5 9
2 6 5
3 5 8
9 7 9

Sample Output 1

56

Consider having the 2-nd, 4-th and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:

Beauty: 1 + 3 + 9 = 13

Tastiness: 5 + 5 + 7 = 17

Popularity: 9 + 8 + 9 = 26

The value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 13 + 17 + 26 = 56. This is the maximum value.

Sample Input 2

5 3
1 -2 3
-4 5 -6
7 -8 -9
-10 11 -12
13 -14 15

Sample Output 2

54

Consider having the 1-st, 3-rd and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:

Beauty: 1 + 7 + 13 = 21

Tastiness: (-2) + (-8) + (-14) = -24

Popularity: 3 + (-9) + 15 = 9

The value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 21 + 24 + 9 = 54. This is the maximum value.

Sample Input 3

10 5
10 -80 21
23 8 38
-94 28 11
-26 -2 18
-69 72 79
-26 -86 -54
-72 -50 59
21 65 -32
40 -94 87
-62 18 82

Sample Output 3

638

If we have the 3-rd, 4-th, 5-th, 7-th and 10-th kinds of cakes, the total beauty, tastiness and popularity will be -323, 66 and 249, respectively.

The value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 323 + 66 + 249 = 638. This is the maximum value.

Sample Input 4

3 2
2000000000 -9000000000 4000000000
7000000000 -5000000000 3000000000
6000000000 -1000000000 8000000000

Sample Output 4

30000000000

The values of the beauty, tastiness and popularity of the cakes and the value to be printed may not fit into 32-bit integers.


N = int(input())
if N <= 999:
    print("ABC")
else:
    print("ABD")

Score : 100 points

Problem Statement

Decades have passed since the beginning of AtCoder Beginner Contest.

The contests are labeled as ABC001, ABC002, ... from the first round, but after the 999-th round ABC999, a problem occurred: how the future rounds should be labeled?

In the end, the labels for the rounds from the 1000-th to the 1998-th are decided: ABD001, ABD002, ..., ABD999.

You are given an integer N between 1 and 1998 (inclusive). Print the first three characters of the label of the N-th round of AtCoder Beginner Contest.

Constraints

1 \leq N \leq 1998

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the first three characters of the label of the N-th round of AtCoder Beginner Contest.

Sample Input 1

999

Sample Output 1

ABC

The 999-th round of AtCoder Beginner Contest is labeled as ABC999.

Sample Input 2

1000

Sample Output 2

ABD

The 1000-th round of AtCoder Beginner Contest is labeled as ABD001.

Sample Input 3

1481

Sample Output 3

ABD

The 1481-th round of AtCoder Beginner Contest is labeled as ABD482.


N = input()

if len(N) < 4:
    print("ABC")
else:
    print("ABD")


a,b=map(int,input().split())
print(sum(i for i in range(b-a))-a)

Score : 200 points

Problem Statement

In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.

It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.

Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.

Assume also that the depth of the snow cover is always at least 1 meter.

Constraints

1 \leq a < b < 499500(=1+2+3+...+999)

All values in input are integers.

There is no input that contradicts the assumption.

Input

Input is given from Standard Input in the following format:

a b

Output

If the depth of the snow cover is x meters, print x as an integer.

Sample Input 1

8 13

Sample Output 1

2

The heights of the two towers are 10 meters and 15 meters, respectively.
Thus, we can see that the depth of the snow cover is 2 meters.

Sample Input 2

54 65

Sample Output 2

1


a, b = map(int, input().split())
l = []
for i in range(1, 1000):
	l.append(i*(i+1)//2)
for i in range(1, 1000):
	if a+i in l and b+i in l:
		print(i)
		break


from math import log
n = int(input())

def make_list(n, x):
    return [x ** i for i in range(1, int(log(n, x))+1)]

sixes = make_list(n, 6)
nines = make_list(n, 9)
nums = [1] + sixes + nines

dp = [float('inf')] * (n+1)
for num in nums:
    for i in range(1, n+1):
        if i == num:
            dp[i] = 1
        elif i > num:
            dp[i] = min(dp[i], dp[i-num]+1)
print(dp[n])

Score : 300 points

Problem Statement

To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:

1 yen (the currency of Japan)

6 yen, 6^2(=36) yen, 6^3(=216) yen, ...

9 yen, 9^2(=81) yen, 9^3(=729) yen, ...

At least how many operations are required to withdraw exactly N yen in total?

It is not allowed to re-deposit the money you withdrew.

Constraints

1 \leq N \leq 100000

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If at least x operations are required to withdraw exactly N yen in total, print x.

Sample Input 1

127

Sample Output 1

4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.

Sample Input 2

3

Sample Output 2

3

By withdrawing 1 yen three times, we can withdraw 3 yen in three operations.

Sample Input 3

44852

Sample Output 3

16


n = int(input())
def f(x):
    x%10+f(x//10) if x else 0
print(min([f(i)+f(n-i) for i in range(0,n+1)]))

Score : 200 points

Problem Statement

Takahashi has two positive integers A and B.

It is known that A plus B equals N.
Find the minimum possible value of "the sum of the digits of A" plus "the sum of the digits of B" (in base 10).

Constraints

2 ≤ N ≤ 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum possible value of "the sum of the digits of A" plus "the sum of the digits of B".

Sample Input 1

15

Sample Output 1

6

When A=2 and B=13, the sums of their digits are 2 and 4, which minimizes the value in question.

Sample Input 2

100000

Sample Output 2

10


import math, sys
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict, deque
from copy import deepcopy
from functools import lru_cache
from heapq import heapify, heappop, heappush
from itertools import accumulate, combinations, permutations
input = sys.stdin.readline
mod = 10**9 + 7
ns = lambda: input().strip()
ni = lambda: int(input().strip())
nm = lambda: map(int, input().split())
nl = lambda: list(map(int, input().split()))

a, b = nm()

print(max([a + b, a - b, a * b]))

Score : 100 points

Problem Statement

You are given two integers A and B.
Find the largest value among A+B, A-B and A \times B.

Constraints

-1000 \leq A,B \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B

Output

Print the largest value among A+B, A-B and A \times B.

Sample Input 1

3 1

Sample Output 1

4

3+1=4, 3-1=2 and 3 \times 1=3. The largest among them is 4.

Sample Input 2

4 -2

Sample Output 2

6

The largest is 4 - (-2) = 6.

Sample Input 3

0 0

Sample Output 3

0


a,b = map(int,input().split())

print(max(a+b, a-b, a*b))


n=int(input())
s=list(input().strip())
ans=0
for i in range(n):
  s1=set(s[:i])
  s2=set(s[i:])
  ans=max(ans,len(s1 & s2))
print(ans)

Score : 200 points

Problem Statement

You are given a string S of length N consisting of lowercase English letters.
We will cut this string at one position into two strings X and Y.
Here, we would like to maximize the number of different letters contained in both X and Y.
Find the largest possible number of different letters contained in both X and Y when we cut the string at the optimal position.

Constraints

2 \leq N \leq 100

|S| = N

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the largest possible number of different letters contained in both X and Y.

Sample Input 1

6
aabbca

Sample Output 1

2

If we cut the string between the third and fourth letters into X = aab and Y = bca, the letters contained in both X and Y are a and b.
There will never be three or more different letters contained in both X and Y, so the answer is 2.

Sample Input 2

10
aaaaaaaaaa

Sample Output 2

1

However we divide S, only a will be contained in both X and Y.

Sample Input 3

45
tgxgdqkyjzhyputjjtllptdfxocrylqfqjynmfbfucbir

Sample Output 3

9


n = int(input())
S = [s for s in input()]
ans = float('inf')
for i in range(n):
    #print(S[:i],S[i+1:])
    ans = min(ans,S[:i].count('W')+S[i+1:].count('E'))
print(ans)

Score : 300 points

Problem Statement

There are N people standing in a row from west to east.
Each person is facing east or west.
The directions of the people is given as a string S of length N.
The i-th person from the west is facing east if S_i = E, and west if S_i = W.

You will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.
Here, we do not care which direction the leader is facing.

The people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.
Find the minimum number of people who have to change their directions.

Constraints

2 \leq N \leq 3 \times 10^5

|S| = N

S_i is E or W.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the minimum number of people who have to change their directions.

Sample Input 1

5
WEEWW

Sample Output 1

1

Assume that we appoint the third person from the west as the leader.
Then, the first person from the west needs to face east and has to turn around.
The other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.
It is not possible to have 0 people who have to change their directions, so the answer is 1.

Sample Input 2

12
WEWEWEEEWWWE

Sample Output 2

4

Sample Input 3

8
WWWWWEEE

Sample Output 3

3


a,b,c,d = map(int,input().split())
if abs(a-c) <= d or (abs(a-b) <= d and abs(b-c)<=d):
    print('Yes')
else:
    print('No')

Score : 100 points

Problem Statement

Three people, A, B and C, are trying to communicate using transceivers.
They are standing along a number line, and the coordinates of A, B and C are a, b and c (in meters), respectively.
Two people can directly communicate when the distance between them is at most d meters.
Determine if A and C can communicate, either directly or indirectly.
Here, A and C can indirectly communicate when A and B can directly communicate and also B and C can directly communicate.

Constraints

1 ≤ a,b,c ≤ 100

1 ≤ d ≤ 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

a b c d

Output

If A and C can communicate, print Yes; if they cannot, print No.

Sample Input 1

4 7 9 3

Sample Output 1

Yes

A and B can directly communicate, and also B and C can directly communicate, so we should print Yes.

Sample Input 2

100 10 1 2

Sample Output 2

No

They cannot communicate in this case.

Sample Input 3

10 10 10 1

Sample Output 3

Yes

There can be multiple people at the same position.

Sample Input 4

1 100 2 10

Sample Output 4

Yes


import sys
X = int(input())
L = []
for i in range(1,32):
  for j in range(2,10):
    if X <= i**j:
      L.append(i**(j-1))
      break
print(max(L))

Score : 200 points

Problem Statement

You are given a positive integer X.
Find the largest perfect power that is at most X.
Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

1 ≤ X ≤ 1000

X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the largest perfect power that is at most X.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961


from collections import Counter
def main():
    s=input()
    k=int(input())
    p=sorted(Counter(s).items(), key=lambda x: x[1], reverse=True)
    count = 1
    for i in range(len(p)):
        for t in g(p[i][0], s):
            if count == k:
                print(t)
                return
            count += 1

def g(s, ss):
    sumi = set()
    lens = len(ss)
    for l in range(lens):
        for i in range(lens):
            if i+l >= lens:
                break
            res = ss[i:i+l+1]
            if (ss[i] == s) and (res not in sumi):
                sumi.add(res)
    return sorted(sumi)

if __name__ == "__main__":
    main()

Score : 300 points

Problem Statement

You are given a string s.
Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.
Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 ≤ |s| ≤ 5000

s consists of lowercase English letters.

1 ≤ K ≤ 5

s has at least K different substrings.

Partial Score

200 points will be awarded as a partial score for passing the test set satisfying |s| ≤ 50.

Input

Input is given from Standard Input in the following format:

s
K

Output

Print the K-th lexicographically smallest substring of K.

Sample Input 1

aba
4

Sample Output 1

b

s has five substrings: a, b, ab, ba and aba.
Among them, we should print the fourth smallest one, b.
Note that we do not count a twice.

Sample Input 2

atcoderandatcodeer
5

Sample Output 2

andat

Sample Input 3

z
1

Sample Output 3

z


#encoding utf-8

import copy
import numpy as np
import random

s = list(str(input()))
k = int(input())

substrings = []
for length in range(1,len(s)+1):
    if length >= 5:
        break
    for i in range(len(s)-length+1):
        word = "".join(s[i:i+length])
        # print(word)
        if word in substrings:
            pass
        else:
            substrings.append(str(word))

substrings.sort()
# print(substrings)
print(substrings[k-1])


def find(x):
    while union[x] != x:
        x = union[x]
    return x

N, M = map(int, input().split())
p = list(map(int, input().split()))

union = [i for i in range(N+1)]

for i in range(M):
    x, y = map(int, input().split())
    a, b = find(x), find(y)
    if a != b:
        union[a] = b

ans = 0
for idx, n in enumerate(p):
    x, y = find(idx+1), find(n)
    if x == y:
        ans += 1

print(ans)

Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 ≤ i ≤ N) such that p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

Find the maximum possible number of i such that p_i = i after operations.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.
Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation.


H,W = map(int,raw_input().split())

s = []
for i in range(H):
	s.append(raw_input())

flag=True
for i in range(H):
	for j in range(W):
		if s[i][j]=='#':
			local_flag=False
			if i+1<H:
				if s[i+1][j]=='#':
					local_flag=True
			if j+1<W:
				if s[i][j+1]=='#':
					local_flag=True
			if i-1>=0:
				if s[i-1][j]=='#':
					local_flag=True
			if j-1>=0:
				if s[i][j-1]=='#':
					local_flag=True
			if local_flag==False:
				flag=False
if flag:
	print 'Yes'
else:
	print 'No'

Score: 300 points

Problem Statement

We have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).

Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= #, and to make Square (i, j) white when s_{i, j}= ..

However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.

Determine if square1001 can achieve his objective.

Constraints

H is an integer between 1 and 50 (inclusive).

W is an integer between 1 and 50 (inclusive).

For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W), s_{i, j} is # or ..

Input

Input is given from Standard Input in the following format:

H W
s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W}
s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W}
: :
s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W}

Output

If square1001 can achieve his objective, print Yes; if he cannot, print No.

Sample Input 1

3 3
.#.
###
.#.

Sample Output 1

Yes

One possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars.

Sample Input 2

5 5
#.#.#
.#.#.
#.#.#
.#.#.
#.#.#

Sample Output 2

No

square1001 cannot achieve his objective here.

Sample Input 3

11 11
...#####...
.##.....##.
#..##.##..#
#..##.##..#
#.........#
#...###...#
.#########.
.#.#.#.#.#.
##.#.#.#.##
..##.#.##..
.##..#..##.

Sample Output 3

Yes


h,w = map(int, input().split())
s = [input() for _ in range(h)]

def check():
    for i in range(h):
        for j in range(w):
            if s[i][j] == '.':
                continue
            ok = False
            for x,y in [(i-1,j), (i+1,j), (i,j+1), (i,j-1)]:
                if x<0 or x>=h or y<0 or y>=w :
                    continue
                if s[x][y] == '#':
                    ok = True
            if not ok:
                return False
    return True

print("Yes" if check() else "No")


# Nまでの素数を列挙
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int type.")
    if n < 2:
        raise ValueError("n is more than 2")
    prime = [2]
    limit = int(n ** 0.5)
    data = [i + 1 for i in range(2, n, 2)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]

# if __name__ == '__main__':
# data = get_sieve_of_eratosthenes(100)
# print(' '.join(map(str, data)))
# print("2～{0}までで以上が素数です\n".format(100))

N = int(input())
P = get_sieve_of_eratosthenes(55555)
cnt = 0
for p in P:
    if p % 5 == 1:
        print(p)
        cnt += 1
    if cnt == N:
        break

Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79


from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

MOD = 10**9 + 7

N = read()

NN = N + 1
fact = [1] * NN
for i in range(1, NN):
  fact[i] = (fact[i-1] * i) % MOD

def inv(n):
  return pow(n, MOD-2, MOD)

def comb(n, k):
  return fact[n] * inv(fact[n-k]) % MOD * inv(fact[k]) % MOD

S = [0] * N
for k in range((N+1) // 2, N):
  c = comb(k-1, N-1-k)
  S[k] = c * fact[k] % MOD

# print(S, file=stderr)

ans = 0
for k in range((N+1) // 2, N):
  ans = (ans + k * (S[k] - S[k-1] * (N - k)) % MOD) % MOD
print(ans)

Score : 800 points

Problem Statement

There are N squares lining up in a row, numbered 1 through N from left to right.
Initially, all squares are white.
We also have N-1 painting machines, numbered 1 through N-1.
When operated, Machine i paints Square i and i+1 black.

Snuke will operate these machines one by one.
The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.

Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P.
Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations.
Find the sum of the scores over all possible permutations for him.
Since this can be extremely large, compute the sum modulo 10^9+7.

Constraints

2 \leq N \leq 10^6

Input

Input is given from Standard Input in the following format:

N

Output

Print the sum of the scores over all possible permutations, modulo 10^9+7.

Sample Input 1

4

Sample Output 1

16

There are six possible permutations as P.
Among them, P = (1, 3, 2) and P = (3, 1, 2) have a score of 2, and the others have a score of 3.
Thus, the answer is 2 \times 2 + 3 \times 4 = 16.

Sample Input 2

2

Sample Output 2

1

There is only one possible permutation: P = (1), which has a score of 1.

Sample Input 3

5

Sample Output 3

84

Sample Input 4

100000

Sample Output 4

341429644


s = input()
s = list(s)
count = 0
for i in s:
    if i == "o":
        count += 1

print(700 + 100 * count)

Score : 100 points

Problem Statement

In "Takahashi-ya", a ramen restaurant, a bowl of ramen costs 700 yen (the currency of Japan), plus 100 yen for each kind of topping (boiled egg, sliced pork, green onions).

A customer ordered a bowl of ramen and told which toppings to put on his ramen to a clerk. The clerk took a memo of the order as a string S. S is three characters long, and if the first character in S is o, it means the ramen should be topped with boiled egg; if that character is x, it means the ramen should not be topped with boiled egg. Similarly, the second and third characters in S mean the presence or absence of sliced pork and green onions on top of the ramen.

Write a program that, when S is given, prints the price of the corresponding bowl of ramen.

Constraints

S is a string of length 3.

Each character in S is o or x.

Input

Input is given from Standard Input in the following format:

S

Output

Print the price of the bowl of ramen corresponding to S.

Sample Input 1

oxo

Sample Output 1

900

The price of a ramen topped with two kinds of toppings, boiled egg and green onions, is 700 + 100 \times 2 = 900 yen.

Sample Input 2

ooo

Sample Output 2

1000

The price of a ramen topped with all three kinds of toppings is 700 + 100 \times 3 = 1000 yen.

Sample Input 3

xxx

Sample Output 3

700

The price of a ramen without any toppings is 700 yen.


price_A, price_B, price_AB, num_A, num_B = map(int,input().split())
AandB = price_A * num_A + price_B * num_B
if num_A >= num_B:
    minAB = price_AB*num_B*2 + price_A*(num_A-num_B)
else:
    minAB = price_AB*num_A*2 + price_B*(num_B-num_A)
maxAB = price_AB * max(num_A, num_B) * 2
print(min(AandB, minAB, maxAB))

Score : 300 points

Problem Statement

"Pizza At", a fast food chain, offers three kinds of pizza: "A-pizza", "B-pizza" and "AB-pizza". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.

Nakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.

Constraints

1 ≤ A, B, C ≤ 5000

1 ≤ X, Y ≤ 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C X Y

Output

Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.

Sample Input 1

1500 2000 1600 3 2

Sample Output 1

7900

It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.

Sample Input 2

1500 2000 1900 3 2

Sample Output 2

8500

It is optimal to directly buy three A-pizzas and two B-pizzas.

Sample Input 3

1500 2000 500 90000 100000

Sample Output 3

100000000

It is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.


def solve(a,b,c,x,y):
  l = []
  for i in range(5*(10**4)+1):
    s = a*max(x-i,0)+b*max(y-i,0)+c*i*2
    l.append(s)
  return min(l)

A,B,C,X,Y = map(int,input().split())
print(solve(A,B,C,X,Y))


import sys
input = sys.stdin.readline

A, B, C, X, Y = map(int, input().split(' '))
set_price = min(A+B, C*2)
set_num = min(X, Y)

ans = set_price * set_num
if X > Y:
    ans += min(A, C*2) * (X-Y)
elif X < Y:
    ans += min(B, C*2) * (Y-X)
print(ans)


a,b,x=map(int,raw_input().split())
if a+(x-a) ==x or a==x:
  print "YES"
else:
  print "NO"

Score : 100 points

Problem Statement

There are a total of A + B cats and dogs.
Among them, A are known to be cats, but the remaining B are not known to be either cats or dogs.

Determine if it is possible that there are exactly X cats among these A + B animals.

Constraints

1 \leq A \leq 100

1 \leq B \leq 100

1 \leq X \leq 200

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B X

Output

If it is possible that there are exactly X cats, print YES; if it is impossible, print NO.

Sample Input 1

3 5 4

Sample Output 1

YES

If there are one cat and four dogs among the B = 5 animals, there are X = 4 cats in total.

Sample Input 2

2 2 6

Sample Output 2

NO

Even if all of the B = 2 animals are cats, there are less than X = 6 cats in total.

Sample Input 3

5 3 2

Sample Output 3

NO

Even if all of the B = 3 animals are dogs, there are more than X = 2 cats in total.


A,B,X=map(int,input().split())
if A<=X and X<=A+B:
  print("YES")
else:
  print("NO")


import numpy as np

n, m, x = map(int, input().split())
a_list = np.array(list(map(int, input().split())))

upper = np.sum((a_list > x))
lower = len(a_list) - upper

print(min(lower, upper))

Score : 200 points

Problem Statement

There are N + 1 squares arranged in a row, numbered 0, 1, ..., N from left to right.

Initially, you are in Square X.
You can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.
However, for each i = 1, 2, ..., M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.
It is guaranteed that there is no toll gate in Square 0, Square X and Square N.

Find the minimum cost incurred before reaching the goal.

Constraints

1 \leq N \leq 100

1 \leq M \leq 100

1 \leq X \leq N - 1

1 \leq A_1 < A_2 < ... < A_M \leq N

A_i \neq X

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M X
A_1 A_2 ... A_M

Output

Print the minimum cost incurred before reaching the goal.

Sample Input 1

5 3 3
1 2 4

Sample Output 1

1

The optimal solution is as follows:

First, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.

Then, travel from Square 4 to Square 5. This time, no cost is incurred.

Now, we are in Square 5 and we have reached the goal.

In this case, the total cost incurred is 1.

Sample Input 2

7 3 2
4 5 6

Sample Output 2

0

We may be able to reach the goal at no cost.

Sample Input 3

10 7 5
1 2 3 4 6 8 9

Sample Output 3

3


_,M,X = list(map(int,input().split()))
a = list(map(int,input().split()))
for i,c in enumerate(a):
    if X < c:
        print(min(i,M-i))
        break


import sys
if __name__ == "__main__":
    N = int(input())
    X = list(map(int, (input().split(' '))))
    buf = sorted(X)
    for i in range(N):
#        buf = list(X)
#        buf.pop(i)
#        buf = sorted(buf)
#        print(X[i])
#        print(buf[int(N/2)])
        if X[i] < buf[int(N/2)]:
            print(buf[int(N/2)])
        else:
            print(buf[int(N/2)-1])

Score : 300 points

Problem Statement

When l is an odd number, the median of l numbers a_1, a_2, ..., a_l is the (\frac{l+1}{2})-th largest value among a_1, a_2, ..., a_l.

You are given N numbers X_1, X_2, ..., X_N, where N is an even number.
For each i = 1, 2, ..., N, let the median of X_1, X_2, ..., X_N excluding X_i, that is, the median of X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N be B_i.

Find B_i for each i = 1, 2, ..., N.

Constraints

2 \leq N \leq 200000

N is even.

1 \leq X_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample Output 1

4
3
3
4

Since the median of X_2, X_3, X_4 is 4, B_1 = 4.

Since the median of X_1, X_3, X_4 is 3, B_2 = 3.

Since the median of X_1, X_2, X_4 is 3, B_3 = 3.

Since the median of X_1, X_2, X_3 is 4, B_4 = 4.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4


n=int(input())
a=sorted(list(map(int,input().split())))
b=a.pop(-1)
d=0
e=0
for i in [n//2-1,n//2]:
    c=1
    A=a[i]
    for j in range(i+1)[A:i+1]:
        c*=j
    for k in range(1,A+1):
        c/=k
    if d < c:
        d=c
        e=A
print(b,e)

Score : 400 points

Problem Statement

Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order.
From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized.
If there are multiple pairs that maximize the value, any of them is accepted.

Constraints

2 \leq n \leq 10^5

0 \leq a_i \leq 10^9

a_1,a_2,...,a_n are pairwise distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print a_i and a_j that you selected, with a space in between.

Sample Input 1

5
6 9 4 2 11

Sample Output 1

11 6

\rm{comb}(a_i,a_j) for each possible selection is as follows:

\rm{comb}(4,2)=6

\rm{comb}(6,2)=15

\rm{comb}(6,4)=15

\rm{comb}(9,2)=36

\rm{comb}(9,4)=126

\rm{comb}(9,6)=84

\rm{comb}(11,2)=55

\rm{comb}(11,4)=330

\rm{comb}(11,6)=462

\rm{comb}(11,9)=55

Thus, we should print 11 and 6.

Sample Input 2

2
100 0

Sample Output 2

100 0


import sys

stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().strip()

n = ni()
a = na()

if n == 2:
    if a[0] > a[1]:
        print(a[0],a[1])
    else:
        print(a[1],a[0])
else:
    x = max(a)
    mid = x / 2
    a.remove(x)

    diff = mid - a[0]
    ans = 0
    for i in range(len(a)):
        if diff > abs(mid - a[i]):
            diff = abs(mid - a[i])
            ans = i
    print(x,a[ans])


#coding:utf-8
n=[int(i) for i in input().split()]
if(n[1]-n[0]+1<=2*n[2]):
  for i in range(n[0],n[1]+1):
    print(i)
else:
  for j in range(n[0],n[0]+n[2]):
    print(j)
  for k in range(n[1]-n[2]+1,n[1]+1):
    print(k)

Score : 100 points

Problem Statement

You are given a string S of length 3 consisting of a, b and c. Determine if S can be obtained by permuting abc.

Constraints

|S|=3

S consists of a, b and c.

Input

Input is given from Standard Input in the following format:

S

Output

If S can be obtained by permuting abc, print Yes; otherwise, print No.

Sample Input 1

bac

Sample Output 1

Yes

Swapping the first and second characters in bac results in abc.

Sample Input 2

bab

Sample Output 2

No

Sample Input 3

abc

Sample Output 3

Yes

Sample Input 4

aaa

Sample Output 4

No


import sys
import math
import collections
import itertools
import array
import inspect

# Set max recursion limit
sys.setrecursionlimit(10000)

# Debug output

def chkprint(*args):
    names = {id(v): k for k, v in inspect.currentframe().f_back.f_locals.items()}
    print(', '.join(names.get(id(arg), '???')+' = '+repr(arg) for arg in args))

# Binary converter

def to_bin(x):
    return bin(x)[2:]

def li_input():
    return [int(_) for _ in input().split()]

# --------------------------------------------

dp = None

def main():
    A, B, K = li_input()

    C = []

    for i in range(A, A + K):
        C.append(i)

    for i in range(B - K + 1, B + 1):
        if i not in C:
            C.append(i)

    for c in C:
        print(c)

main()

Score : 200 points

Problem Statement

Print all the integers that satisfies the following in ascending order:

Among the integers between A and B (inclusive), it is either within the K smallest integers or within the K largest integers.

Constraints

1 \leq A \leq B \leq 10^9

1 \leq K \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B K

Output

Print all the integers that satisfies the condition above in ascending order.

Sample Input 1

3 8 2

Sample Output 1

3
4
7
8

3 is the first smallest integer among the integers between 3 and 8.

4 is the second smallest integer among the integers between 3 and 8.

7 is the second largest integer among the integers between 3 and 8.

8 is the first largest integer among the integers between 3 and 8.

Sample Input 2

4 8 3

Sample Output 2

4
5
6
7
8

Sample Input 3

2 9 100

Sample Output 3

2
3
4
5
6
7
8
9


import sys
input=sys.stdin.readline

l=list(map(int,input().split()))
a,b,c=sorted(l)
#print(a,b,c)
if a%2==b%2 and a%2==c%2:
    print((2*c-a-b)//2)
elif a%2==b%2:
    print((2*c-2-a-b)//2+1)
else:
    print((2*c+1-a-b)//2+1)

Score : 300 points

Problem Statement

You are given three integers A, B and C. Find the minimum number of operations required to make A, B and C all equal by repeatedly performing the following two kinds of operations in any order:

Choose two among A, B and C, then increase both by 1.

Choose one among A, B and C, then increase it by 2.

It can be proved that we can always make A, B and C all equal by repeatedly performing these operations.

Constraints

0 \leq A,B,C \leq 50

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C

Output

Print the minimum number of operations required to make A, B and C all equal.

Sample Input 1

2 5 4

Sample Output 1

2

We can make A, B and C all equal by the following operations:

Increase A and C by 1. Now, A, B, C are 3, 5, 5, respectively.

Increase A by 2. Now, A, B, C are 5, 5, 5, respectively.

Sample Input 2

2 6 3

Sample Output 2

5

Sample Input 3

31 41 5

Sample Output 3

23


N = int(input())
D, X = map(int, input().split())
ans = X
for i in range(N):
  a = int(input())
  ans += ((D - 1) // a + 1)
print(ans)

Score : 200 points

Problem Statement

Some number of chocolate pieces were prepared for a training camp.
The camp had N participants and lasted for D days.
The i-th participant (1 \leq i \leq N) ate one chocolate piece on each of the following days in the camp: the 1-st day, the (A_i + 1)-th day, the (2A_i + 1)-th day, and so on.
As a result, there were X chocolate pieces remaining at the end of the camp. During the camp, nobody except the participants ate chocolate pieces.

Find the number of chocolate pieces prepared at the beginning of the camp.

Constraints

1 \leq N \leq 100

1 \leq D \leq 100

1 \leq X \leq 100

1 \leq A_i \leq 100 (1 \leq i \leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D X
A_1
A_2
:
A_N

Output

Find the number of chocolate pieces prepared at the beginning of the camp.

Sample Input 1

3
7 1
2
5
10

Sample Output 1

8

The camp has 3 participants and lasts for 7 days.
Each participant eats chocolate pieces as follows:

The first participant eats one chocolate piece on Day 1, 3, 5 and 7, for a total of four.

The second participant eats one chocolate piece on Day 1 and 6, for a total of two.

The third participant eats one chocolate piece only on Day 1, for a total of one.

Since the number of pieces remaining at the end of the camp is one, the number of pieces prepared at the beginning of the camp is 1 + 4 + 2 + 1 = 8.

Sample Input 2

2
8 20
1
10

Sample Output 2

29

Sample Input 3

5
30 44
26
18
81
18
6

Sample Output 3

56


""" AtCoder """

N = int(input())
D, X = map(int, input().split())
A = [int(input()) for _ in range(N)]

ans = 0

for i in range(N):
    if D % A[i] > 0:
        ans += D // A[i] + 1
    else:
        ans += D // A[i]

print(ans + X)


N = int(input())
D,X = map(int,input().split())
A = [0]*N
for i in range(N):
    A[i] = int(input())
cnt = 0
for i in range(N):
    cnt += (D-1)//A[i]+1
print(X+cnt)