message stringlengths 2 57.2k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given from Standard Input in the following format:
N
Outp... | instruction | 0 | 49,401 | 22 | 98,802 |
"Correct Solution:
```
N=int(input())
ans=0
for i in range(1,N+1):
ans+=(N//i+1)*i*(N//i)//2
print(ans)
``` | output | 1 | 49,401 | 22 | 98,803 |
Provide a correct Python 3 solution for this coding contest problem.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given from Standard Input in the following format:
N
Outp... | instruction | 0 | 49,402 | 22 | 98,804 |
"Correct Solution:
```
n = int(input())
ans = 0
for i in range(1, n+1):
d = n // i
ans += d*(d+1)//2*i
print(ans)
``` | output | 1 | 49,402 | 22 | 98,805 |
Provide a correct Python 3 solution for this coding contest problem.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given from Standard Input in the following format:
N
Outp... | instruction | 0 | 49,403 | 22 | 98,806 |
"Correct Solution:
```
n = int(input())
ans= 0
for i in range(1,n+1):
j = n//i
ans += j*(j+1)*i/2
print(int(ans))
``` | output | 1 | 49,403 | 22 | 98,807 |
Provide a correct Python 3 solution for this coding contest problem.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given from Standard Input in the following format:
N
Outp... | instruction | 0 | 49,404 | 22 | 98,808 |
"Correct Solution:
```
N = int(input())
ans = 0
for i in range(1, N+1):
n = N//i
ans += n*(i+i*n)//2
print(ans)
``` | output | 1 | 49,404 | 22 | 98,809 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,405 | 22 | 98,810 |
Yes | output | 1 | 49,405 | 22 | 98,811 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,406 | 22 | 98,812 |
Yes | output | 1 | 49,406 | 22 | 98,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,407 | 22 | 98,814 |
Yes | output | 1 | 49,407 | 22 | 98,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,408 | 22 | 98,816 |
Yes | output | 1 | 49,408 | 22 | 98,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,409 | 22 | 98,818 |
No | output | 1 | 49,409 | 22 | 98,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,410 | 22 | 98,820 |
No | output | 1 | 49,410 | 22 | 98,821 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,411 | 22 | 98,822 |
No | output | 1 | 49,411 | 22 | 98,823 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer X, let f(X) be the number of positive divisors of X.
Given a positive integer N, find \sum_{K=1}^N K\times f(K).
Constraints
* 1 \leq N \leq 10^7
Input
Input is given... | instruction | 0 | 49,412 | 22 | 98,824 |
No | output | 1 | 49,412 | 22 | 98,825 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yasin has an array a containing n integers. Yasin is a 5 year old, so he loves ultimate weird things.
Yasin denotes weirdness of an array as maximum gcd(ai, aj) value among all 1 ≤ i < j ≤ n. F... | instruction | 0 | 50,111 | 22 | 100,222 |
No | output | 1 | 50,111 | 22 | 100,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yasin has an array a containing n integers. Yasin is a 5 year old, so he loves ultimate weird things.
Yasin denotes weirdness of an array as maximum gcd(ai, aj) value among all 1 ≤ i < j ≤ n. F... | instruction | 0 | 50,112 | 22 | 100,224 |
No | output | 1 | 50,112 | 22 | 100,225 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,265 | 22 | 100,530 |
"Correct Solution:
```
n=int(input())
a=0
for i in range(2,10**6):
b=0
while n%i==0:
n//=i
b+=1
c=d=0
while c+d<b:
c+=1
d+=c
a+=c
print(a+(n>1))
``` | output | 1 | 50,265 | 22 | 100,531 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,266 | 22 | 100,532 |
"Correct Solution:
```
from collections import defaultdict
N=int(input())
soinsu=defaultdict(int)
x=2
while x<=10**6:
while N%x==0:
soinsu[x]+=1
N//=x
x+=1
if N>1:
soinsu[N]+=1
ans=0
for key in soinsu.keys():
x=1
while soinsu[key]>=x:
ans+=1
soinsu[key]-=x
x+=1
print(ans)
``` | output | 1 | 50,266 | 22 | 100,533 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,267 | 22 | 100,534 |
"Correct Solution:
```
n=int(input())
def prime(n):
dic={}
f=2
m=n
while f*f<=m:
r=0
while n%f==0:
n//=f
r+=1
if r>0:
dic[f]=r
f+=1
if n!=1:
dic[n]=1
return dic
def counter(dic):
ans=0
for val in dic.values():
i=1
while i*(i+3)/2<val:
i+=1
ans+=i
... | output | 1 | 50,267 | 22 | 100,535 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,268 | 22 | 100,536 |
"Correct Solution:
```
N = int(input())
primes = {}
for num in range(2, int(N**0.5)+1):
while N%num == 0:
if num in primes:
primes[num] += 1
else:
primes[num] = 1
N //= num
ans = 0
for p in primes.values():
n = 1
while n*(n+1)//2 <= p:
n += 1
ans += n-1
if N > 1:
ans += 1
print(ans... | output | 1 | 50,268 | 22 | 100,537 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,269 | 22 | 100,538 |
"Correct Solution:
```
n = int(input())
a = []
ans = 0
for i in range(2,int(n**0.5)+1):
count = 0
while n%i==0:
n/=i
count+=1
if count!=0:
for j in range(1,count+10):
if j*(j+1)/2>count:
ans+=j-1
break
if n!=1:
ans+=1
print(ans)
``` | output | 1 | 50,269 | 22 | 100,539 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,270 | 22 | 100,540 |
"Correct Solution:
```
import math
n=int(input())
p=2
c=0
curr=0
while n%p==0:
curr+=1
n//=p
j=0
j=(math.sqrt(1+8*curr)-1)//2
c+=int(j)
#print(j)
for i in range (3,int(math.sqrt(n))+1,2):
p=i
curr=0
while n%p==0:
curr+=1
n//=p
j=0
j=(math.sqrt(1+8*curr)-1)//2
c+=int(j)
... | output | 1 | 50,270 | 22 | 100,541 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,271 | 22 | 100,542 |
"Correct Solution:
```
ans = 0
N = int(input())
x = 2
while not N % x:
ans += 1
N //= x
x *= 2
while not N % 2:
N //= 2
i = 3
while i*i <= N:
x = i
while not N % x:
ans += 1
N //= x
x *= i
while not N % i:
N //= i
i += 2
i... | output | 1 | 50,271 | 22 | 100,543 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer... | instruction | 0 | 50,272 | 22 | 100,544 |
"Correct Solution:
```
#import math
n=int(input())
ans=0
p=2
for p in range(2, int((n+0.5)**0.5)+1):
if n%p==0:
cnt=0
while n%p==0:
cnt+=1
n//=p
k=1
while cnt>=k:
cnt-=k
k+=1
ans+=1
if n>1:
ans+=1
print(ans)
``` | output | 1 | 50,272 | 22 | 100,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a positive integer N. Consider repeatedly applying the operation below on N:
* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^... | instruction | 0 | 50,280 | 22 | 100,560 |
No | output | 1 | 50,280 | 22 | 100,561 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,543 | 22 | 101,086 |
Tags: brute force, math, number theory
Correct Solution:
```
a, b = map(int,input().split())
if a < b: a,b=b,a
if a == b: print(0); exit()
def update(g):
global ans
# a+n must be a multiple of g, and so is b+n
if a%g != b%g: return
n = g - a%g if a%g else 0
lcm = (a+n)*(b+n)//g
ans = min(ans, (... | output | 1 | 50,543 | 22 | 101,087 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,544 | 22 | 101,088 |
Tags: brute force, math, number theory
Correct Solution:
```
import math
a, b = map(int,input().split())
if b > a:
a,b=b,a
if not a % b:
print(0)
exit()
else:
sub=a-b
divs = []
for i in range(1, int(math.sqrt(sub))+1):
if sub % i == 0:
divs.append(i)
divs.append(s... | output | 1 | 50,544 | 22 | 101,089 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,545 | 22 | 101,090 |
Tags: brute force, math, number theory
Correct Solution:
```
a,b=list(map(int,input().split()))
(a,b)=min(a,b),max(a,b)
if b<2*a:
if a==b:
print(0)
exit()
print((-a)%(b-a))
exit()
s=[1]
q=b-a
for i in range(2,int((b-a)**(1/2)+2)):
while q%i==0:
t=[j*i for j in s]
for aa i... | output | 1 | 50,545 | 22 | 101,091 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,546 | 22 | 101,092 |
Tags: brute force, math, number theory
Correct Solution:
```
from fractions import gcd
a,b=map(int,input().split())
d=max(a,b)-min(a,b)
c=[float("inf"),1]
e=[1]
for i in range(1,int(d**0.5)+1):
if i**2==d:
e.append(i)
elif d%i==0:
e.append(i)
e.append(d//i)
for i in e:
h=i*((a-1)//i+... | output | 1 | 50,546 | 22 | 101,093 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,547 | 22 | 101,094 |
Tags: brute force, math, number theory
Correct Solution:
```
def gcd(a, b):
return b if a % b == 0 else gcd(b, a % b)
def findans(d):
l, r = 1, 10**20
while l < r:
mid = (l + r) // 2
if mid * d >= m:
r = mid
else:
l = mid + 1
k = l * d - m
lcm = (a +... | output | 1 | 50,547 | 22 | 101,095 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,548 | 22 | 101,096 |
Tags: brute force, math, number theory
Correct Solution:
```
import math
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
def GCD(x,y):
... | output | 1 | 50,548 | 22 | 101,097 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,549 | 22 | 101,098 |
Tags: brute force, math, number theory
Correct Solution:
```
import io, sys, atexit, os
import math as ma
from sys import exit
from decimal import Decimal as dec
from itertools import permutations
def li ():
return list (map (int, input ().split ()))
def num ():
return map (int, input ().split ())
def nu ():
... | output | 1 | 50,549 | 22 | 101,099 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+... | instruction | 0 | 50,550 | 22 | 101,100 |
Tags: brute force, math, number theory
Correct Solution:
```
def make_divisors(n):
divisors = []
for i in range(1, int(n**0.5)+1):
if n % i == 0:
divisors.append(i)
if i != n // i:
divisors.append(n//i)
#divisors.sort(reverse=True)
return divisors
import... | output | 1 | 50,550 | 22 | 101,101 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,551 | 22 | 101,102 |
Yes | output | 1 | 50,551 | 22 | 101,103 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,552 | 22 | 101,104 |
Yes | output | 1 | 50,552 | 22 | 101,105 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,553 | 22 | 101,106 |
Yes | output | 1 | 50,553 | 22 | 101,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,554 | 22 | 101,108 |
Yes | output | 1 | 50,554 | 22 | 101,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,555 | 22 | 101,110 |
No | output | 1 | 50,555 | 22 | 101,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,556 | 22 | 101,112 |
No | output | 1 | 50,556 | 22 | 101,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,557 | 22 | 101,114 |
No | output | 1 | 50,557 | 22 | 101,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k su... | instruction | 0 | 50,558 | 22 | 101,116 |
No | output | 1 | 50,558 | 22 | 101,117 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Bubble Cup hypothesis stood unsolved for 130 years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao managed to reduce the hypothesis to this problem:
Gi... | instruction | 0 | 50,687 | 22 | 101,374 |
Tags: bitmasks, constructive algorithms, dp, math
Correct Solution:
```
T = input()
mod = int(1e9 + 7)
a = map(int, input().split())
c = []
for n in a:
b = (n // 2 + 2)
b = b * b
b //= 4
c.append(str(b % mod))
print(' '.join(c))
``` | output | 1 | 50,687 | 22 | 101,375 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Bubble Cup hypothesis stood unsolved for 130 years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao managed to reduce the hypothesis to this problem:
Gi... | instruction | 0 | 50,688 | 22 | 101,376 |
Tags: bitmasks, constructive algorithms, dp, math
Correct Solution:
```
t = int(input())
a = list(map(int, input().split()))
out = []
for n in a:
ans = (n//2 + 2)
ans = ans*ans
ans //= 4
out.append(ans%1000000007)
print(' '.join(str(x) for x in out))
``` | output | 1 | 50,688 | 22 | 101,377 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Bubble Cup hypothesis stood unsolved for 130 years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao managed to reduce the hypothesis to this problem:
Gi... | instruction | 0 | 50,690 | 22 | 101,380 |
Tags: bitmasks, constructive algorithms, dp, math
Correct Solution:
```
# ===============================================================================================
# importing some useful libraries.
from __future__ import division, print_function
from fractions import Fraction
import sys
import os
from io import ... | output | 1 | 50,690 | 22 | 101,381 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Bubble Cup hypothesis stood unsolved for 130 years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao manage... | instruction | 0 | 50,694 | 22 | 101,388 |
No | output | 1 | 50,694 | 22 | 101,389 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on... | instruction | 0 | 50,711 | 22 | 101,422 |
Tags: binary search, greedy, math, number theory
Correct Solution:
```
from math import gcd
def t_prime(n):
if n == 1:
return False
for p in [2,3,5,7,11,13,17,19,23]:
if p < n and pow(p,n-1,n) != 1:
return False
return True
primes = [i for i in range(2,10**5) if t_prime(i)]
pse... | output | 1 | 50,711 | 22 | 101,423 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on... | instruction | 0 | 50,712 | 22 | 101,424 |
Tags: binary search, greedy, math, number theory
Correct Solution:
```
from math import gcd
def t_prime(n):
if n == 1: return False
for p in [2,3,5,7,11,13,17,19,23]:
if p < n and pow(p,n-1,n) != 1: return False
return True
primes = [i for i in range(2,10**5) if t_prime(i)];pset = ... | output | 1 | 50,712 | 22 | 101,425 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on... | instruction | 0 | 50,713 | 22 | 101,426 |
Tags: binary search, greedy, math, number theory
Correct Solution:
```
from math import gcd
def t_prime(n):
if n == 1: return False
for p in [2,3,5,7,11,13,17,19,23]:
if p < n and pow(p,n-1,n) != 1: return False
return True
primes = [i for i in range(2,10**5) if t_prime(i)];pset = ... | output | 1 | 50,713 | 22 | 101,427 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on... | instruction | 0 | 50,714 | 22 | 101,428 |
Tags: binary search, greedy, math, number theory
Correct Solution:
```
from math import gcd
def t_prime(n):
if n == 1:
return False
for p in [2,3,5,7,11,13,17,19,23]:
if p < n and pow(p,n-1,n) != 1:
return False
return True
primes = [i for i in range(2,10**5) if t_prime(i)]
pse... | output | 1 | 50,714 | 22 | 101,429 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on... | instruction | 0 | 50,715 | 22 | 101,430 |
Tags: binary search, greedy, math, number theory
Correct Solution:
```
from math import gcd
def t_prime(n):
if n == 1: return False
for p in [2,3,5,7,11,13,17,19,23]:
if p < n and pow(p,n-1,n) != 1: return False
return True
primes = [i for i in range(2,10**5) if t_prime(i)];pset = ... | output | 1 | 50,715 | 22 | 101,431 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divi... | instruction | 0 | 50,716 | 22 | 101,432 |
No | output | 1 | 50,716 | 22 | 101,433 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divi... | instruction | 0 | 50,717 | 22 | 101,434 |
No | output | 1 | 50,717 | 22 | 101,435 |
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