{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE BinaryLiterals #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE NumDecimals #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}

import Control.Applicative
import Control.Arrow
import Control.Monad
import Control.Monad.ST

import Data.Char
import Data.List
import Data.Maybe

import qualified Data.ByteString.Char8 as B

import Data.Array.ST.Safe
import Data.STRef

import Debug.Trace
import Text.Printf

readInt = readLn :: IO Int
readInteger = readLn :: IO Integer
readInts = map ( fst . fromJust . B.readInt ) . B.words <$> B.getLine
readIntegers = map ( fst . fromJust . B.readInteger ) . B.words <$> B.getLine

which a b f = if f then a else b
mp [ a, b ] = ( a, b )

modifyArray a i f = writeArray a i =<< f <$> readArray a i

printList [a] = print a
printList (a:as) = putStr ( show a ) >> putChar ' ' >> printList as

main = do
	[ n, k ] <- readInts
	as <- readInts
	mapM_ putStrLn $ map ( which "Yes" "No" ) $ zipWith (<) as ( drop k as )

Score: 300 points

Problem Statement

M-kun is a student in Aoki High School, where a year is divided into N terms.

There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:

For the first through (K-1)-th terms: not given.

For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.

M-kun scored A_i in the exam at the end of the i-th term.

For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.

Constraints

2 \leq N \leq 200000

1 \leq K \leq N-1

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 K
A_1 A_2 A_3 \ldots A_N

Output

Print the answer in N-K lines.

The i-th line should contain Yes if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and No otherwise.

Sample Input 1

5 3
96 98 95 100 20

Sample Output 1

Yes
No

His grade for each term is computed as follows:

3-rd term: (96 \times 98 \times 95) = 893760

4-th term: (98 \times 95 \times 100) = 931000

5-th term: (95 \times 100 \times 20) = 190000

Sample Input 2

3 2
1001 869120 1001

Sample Output 2

No

Note that the output should be No if the grade for the 3-rd term is equal to the grade for the 2-nd term.

Sample Input 3

15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9

Sample Output 3

Yes
Yes
No
Yes
Yes
No
Yes
Yes


main=interact$show.(1000%).tail.map read.words;m%(x:y:l)|x<y,(q,r)<-divMod m x=(r+q*y)%(y:l)|0<1=m%(y:l);m%_ = m

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

Score: 400 points

Problem Statement

To become a millionaire, M-kun has decided to make money by trading in the next N days. Currently, he has 1000 yen and no stocks - only one kind of stock is issued in the country where he lives.

He is famous across the country for his ability to foresee the future. He already knows that the price of one stock in the next N days will be as follows:

A_1 yen on the 1-st day, A_2 yen on the 2-nd day, ..., A_N yen on the N-th day.

In the i-th day, M-kun can make the following trade any number of times (possibly zero), within the amount of money and stocks that he has at the time.

Buy stock: Pay A_i yen and receive one stock.

Sell stock: Sell one stock for A_i yen.

What is the maximum possible amount of money that M-kun can have in the end by trading optimally?

Constraints

2 \leq N \leq 80

100 \leq A_i \leq 200

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the maximum possible amount of money that M-kun can have in the end, as an integer.

Sample Input 1

7
100 130 130 130 115 115 150

Sample Output 1

1685

In this sample input, M-kun has seven days of trading. One way to have 1685 yen in the end is as follows:

Initially, he has 1000 yen and no stocks.

Day 1: Buy 10 stocks for 1000 yen. Now he has 0 yen.

Day 2: Sell 7 stocks for 910 yen. Now he has 910 yen.

Day 3: Sell 3 stocks for 390 yen. Now he has 1300 yen.

Day 4: Do nothing.

Day 5: Buy 1 stock for 115 yen. Now he has 1185 yen.

Day 6: Buy 10 stocks for 1150 yen. Now he has 35 yen.

Day 7: Sell 11 stocks for 1650 yen. Now he has 1685 yen.

There is no way to have 1686 yen or more in the end, so the answer is 1685.

Sample Input 2

6
200 180 160 140 120 100

Sample Output 2

1000

In this sample input, it is optimal to do nothing throughout the six days, after which we will have 1000 yen.

Sample Input 3

2
157 193

Sample Output 3

1216

In this sample input, it is optimal to buy 6 stocks in Day 1 and sell them in Day 2, after which we will have 1216 yen.

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.


{-# LANGUAGE
  ScopedTypeVariables, BangPatterns, TupleSections, ExplicitForAll,
  LambdaCase, MultiWayIf, Unsafe, RecordWildCards, FlexibleContexts, CPP,
  NoMonomorphismRestriction, GADTs, PatternGuards, MagicHash, UnboxedTuples,
  RankNTypes, EmptyDataDecls, EmptyCase, ViewPatterns, PolyKinds,
  TypeFamilies, OverloadedStrings, FlexibleInstances, UndecidableInstances,
  DefaultSignatures, GeneralizedNewtypeDeriving, StandaloneDeriving,
  DeriveGeneric, DeriveFunctor, DeriveDataTypeable, DeriveFoldable,
  DeriveTraversable, DeriveDataTypeable, FlexibleInstances,
  MultiParamTypeClasses, TypeApplications, RecordWildCards,
  NumericUnderscores #-}
{-# OPTIONS_GHC -O2 #-}

#define PHASE_FUSED [1]
#define PHASE_INNER [0]
#define INLINE_FUSED INLINE PHASE_FUSED
#define INLINE_INNER INLINE PHASE_INNER

import Prelude
import Data.Bits
import Data.List
import Data.Maybe
import Data.Tuple
import Data.Ord
import Data.Int
import Data.Word
import Data.Char
import Data.Ratio
import Data.Function
import Data.STRef
import Data.IORef
import Data.Monoid
import Data.Functor
import Data.Functor.Identity
import Data.Data
import Data.Typeable
import GHC.Generics
import System.IO
import System.IO.Unsafe (unsafeDupablePerformIO, unsafePerformIO)
import Control.Arrow
import Control.Applicative
import Control.Monad
import Control.Monad.Primitive
import Control.Monad.State.Strict
import Control.Monad.ST
import Control.Monad.ST.Lazy (strictToLazyST, lazyToStrictST)
import qualified Control.Monad.ST.Lazy as STL
-- import Control.Monad.ST.Safe
import Control.DeepSeq
import Data.Coerce
import qualified Data.ByteString as BSW
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy as BSLW
import qualified Data.ByteString.Lazy.Char8 as BSL
import qualified Data.ByteString.Builder as BSB
import qualified Data.ByteString.Unsafe as BSU
import qualified Data.ByteString.Internal as BSU
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IMS
import qualified Data.IntMap.Lazy as IML
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Storable as VS
import qualified Data.Vector.Storable.Mutable as VSM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Vector.Fusion.Bundle.Monadic as VFBM
import qualified Data.Vector.Fusion.Bundle as VFB
import qualified Data.Vector.Fusion.Stream.Monadic as VFSM
import qualified Data.Vector.Fusion.Bundle.Size as VFBS
import qualified Data.Vector.Fusion.Util as VFU
import qualified Data.Vector.Algorithms.Intro as VAIT
import qualified Data.Attoparsec.ByteString.Char8 as Atto
import Debug.Trace
import Unsafe.Coerce
import Foreign.ForeignPtr
import GHC.Exts (build, Int(..), Int#,
                 (+#), (*#), (-#), (<#), (>=#), (==#), quotRemInt#,
                 remInt#, uncheckedIShiftRL#, andI#, orI#,
                isTrue#, Addr#, Ptr(..))

main :: IO ()
main = do
  n <- readLn @ Int
  as <- getVecULn n rIntS
  print $ VFB.length $ VG.stream $ VU.ifilter (\i a -> even i && odd a) as
  return ()

#define IL(f) {-# INLINE f #-}; f

IL(putBuilder) = BSB.hPutBuilder stdout

printVecInLines, printVecInSpcSepLn ::
  (VG.Vector v a, ShowAsBuilder a) => v a -> IO ()
IL(printVecInLines) = putBuilder . v2BLines
IL(printVecInSpcSepLn) = putBuilder . v2BSpcSepLn

class ShowAsBuilder a where
  showAsBuilder :: a -> BSB.Builder
  default showAsBuilder :: (Show a) => a -> BSB.Builder
  IL(showAsBuilder) = BSB.string8 . show

-- Inconsistent with show
instance (ShowAsBuilder a, VG.Vector v a) => ShowAsBuilder (v a) where
  IL(showAsBuilder) = v2BSpcSep

#define INS(t,f) instance ShowAsBuilder t where { IL(showAsBuilder)=f }
INS(Int,BSB.intDec)
INS(Int8,BSB.int8Dec)
INS(Int16,BSB.int16Dec)
INS(Int32,BSB.int32Dec)
INS(Int64,BSB.int64Dec)
INS(Word,BSB.wordDec)
INS(Word8,BSB.word8Dec)
INS(Word16,BSB.word16Dec)
INS(Word32,BSB.word32Dec)
INS(Word64,BSB.word64Dec)
INS(Integer,BSB.integerDec)
INS(Float,BSB.floatDec)
INS(Double,BSB.doubleDec)
-- INS(String,BSB.string8) -- Inconsistent with Show
-- INS(BS.ByteString,BSB.byteString) -- Inconsistent with Show
-- INS(BSL.ByteString,BSB.lazyByteString) -- Inconsisitent with Show
#undef INS

-- Inconsistent with Show
instance (ShowAsBuilder a, ShowAsBuilder b) => ShowAsBuilder (a,b) where
  IL(showAsBuilder) = showTupAsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c) =>
  ShowAsBuilder (a,b,c) where
  IL(showAsBuilder) = showTup3AsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  ShowAsBuilder (a,b,c,d) where
  IL(showAsBuilder) = showTup4AsBuilder

IL(showTupAsBuilderWith)
  :: (a -> BSB.Builder) -> (b -> BSB.Builder) -> (a,b) -> BSB.Builder
showTupAsBuilderWith showA showB
  = \(a,b) -> (showA a <>) $ BSB.char7 ' ' <> showB b
IL(showTupAsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b)
  => (a,b) -> BSB.Builder
showTupAsBuilder = showTupAsBuilderWith showAsBuilder showAsBuilder

IL(showTup3AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (a,b,c) -> BSB.Builder
showTup3AsBuilderWith showA showB showC
  = \(a,b,c) -> (showA a <>) $ (BSB.char7 ' ' <>) $ (showB b <>)
                $ (BSB.char7 ' ' <>) $ showC c
IL(showTup3AsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c)
  => (a,b,c) -> BSB.Builder
showTup3AsBuilder
  = showTup3AsBuilderWith showAsBuilder showAsBuilder showAsBuilder

IL(showTup4AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (d -> BSB.Builder) -> (a,b,c,d) -> BSB.Builder
showTup4AsBuilderWith showA showB showC showD
  = \(a,b,c,d) -> (showA a <>) $ (BSB.char7 ' ' <>)
                  $ showTup3AsBuilderWith showB showC showD (b,c,d)
IL(showTup4AsBuilder) ::
  (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  (a,b,c,d) -> BSB.Builder
showTup4AsBuilder = showTup4AsBuilderWith showAsBuilder showAsBuilder
                    showAsBuilder showAsBuilder

v2BSpcSepLn, v2BSpcSep, v2BConcat, v2BLines ::
  (VG.Vector v a, ShowAsBuilder a)
  => v a -> BSB.Builder
IL(v2BSpcSepLn) = v2BSpcSepLnWith showAsBuilder
IL(v2BSpcSep) = v2BSpcSepWith showAsBuilder
IL(v2BConcat) = v2BConcatWith showAsBuilder
IL(v2BLines) = v2BLinesWith showAsBuilder

v2BSpcSepLnWith, v2BSpcSepWith, v2BConcatWith, v2BLinesWith ::
  (VG.Vector v a)
  => (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepLnWith) = v2BSpcSepPostfWith $ BS.singleton '\n'
IL(v2BSpcSepWith) = v2BSpcSepPostfWith BS.empty
IL(v2BConcatWith) showFct = VG.foldr ((<>) . showFct) mempty
IL(v2BLinesWith) showFct
  = VG.foldr (\ a -> (showFct a <>) . (BSB.char7 '\n' <>)) mempty

v2BSpcSepPostf :: (VG.Vector v a, ShowAsBuilder a)
  => BS.ByteString -- ^ postfix
  -> v a -> BSB.Builder
IL(v2BSpcSepPostf) = (`v2BSpcSepPostfWith` showAsBuilder)

v2BSpcSepPostfWith :: (VG.Vector v a)
  => BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepPostfWith) = vecToBuilder BS.empty $ BS.singleton ' '

IL(vecToBuilder) :: (VG.Vector v a)
  => BS.ByteString -- ^ prefix
  -> BS.ByteString -- ^ separator
  -> BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder !prefix !separator !postfix
  = vecToBuilder_ (BSB.byteString prefix)
                  (BSB.byteString separator)
                  (BSB.byteString postfix)

IL(vecToBuilder_) :: (VG.Vector v a)
  => BSB.Builder -- ^ prefix
  -> BSB.Builder -- ^ separator
  -> BSB.Builder -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder_ !prefix !separator !postfix showFct = \vec -> prefix <>
  VG.foldr
  (\ a rest !prefx -> prefx <> (showFct a <> rest separator))
  (const postfix) vec mempty

IL(evalVals) :: [a] -> [a]
evalVals xs = build $ \c n -> foldr (c $!) n xs
IL(forceVals) :: (NFData a) => [a] -> [a]
forceVals xs = build $ \c n -> foldr (c $!!) n xs

IL(readLnWith) :: StateT BS.ByteString Maybe a -> IO a
readLnWith parser = fromJust . evalStateT parser <$> BS.getLine
IL(readContentWith) :: StateT BSL.ByteString Maybe a -> IO a
readContentWith parser = fromJust . evalStateT parser <$> BSL.getContents

IL(getVecGLn) :: (VG.Vector v a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (v a)
getVecGLn n s = VG.unfoldrN n (runStateT s) <$> BS.getLine
IL(getVecGRest) :: (VG.Vector v a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (v a)
getVecGRest n s = VG.unfoldrN n (runStateT s) <$> BSL.getContents
IL(getVecLn) :: Int -> StateT BS.ByteString Maybe a -> IO (V.Vector a)
getVecLn = getVecGLn
IL(getVecRest) :: Int -> StateT BSL.ByteString Maybe a -> IO (V.Vector a)
getVecRest = getVecGRest
IL(getVecULn) :: (VU.Unbox a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (VU.Vector a)
getVecULn = getVecGLn
IL(getVecURest) :: (VU.Unbox a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (VU.Vector a)
getVecURest = getVecGRest

IL(rIntL) :: StateT BSL.ByteString Maybe Int
rIntL = skipSpecialL $ StateT BSL.readInt
IL(rIntS) :: StateT BS.ByteString Maybe Int
rIntS = skipSpecialS $ StateT BS.readInt
IL(rStrL) :: (MonadState BSL.ByteString m) => m BS.ByteString
rStrL = skipSpecialL $ BSL.toStrict <$> state (BSL.span (>='!'))
IL(rStrS) :: (MonadState BS.ByteString m) => m BS.ByteString
rStrS = skipSpecialS $ state $ BS.span (>='!')
IL(rCharL) :: StateT BSL.ByteString Maybe Char
rCharL = StateT BSL.uncons
IL(rCharS) :: StateT BS.ByteString Maybe Char
rCharS = StateT BS.uncons
IL(rCharWL) :: StateT BSL.ByteString Maybe Word8
rCharWL = StateT BSLW.uncons
IL(rCharWS) :: StateT BS.ByteString Maybe Word8
rCharWS = StateT BSW.uncons
IL(dropSpecialL) :: (MonadState BSL.ByteString m) => m ()
dropSpecialL = modify $ BSL.dropWhile (<'!')
IL(dropSpecialS) :: (MonadState BS.ByteString m) => m ()
dropSpecialS = modify $ BS.dropWhile (<'!')
IL(skipSpecialL) :: (MonadState BSL.ByteString m) => m a -> m a
skipSpecialL = (dropSpecialL *>)
IL(skipSpecialS) :: (MonadState BS.ByteString m) => m a -> m a
skipSpecialS = (dropSpecialS *>)

IL(linToMat) :: (VG.Vector v a) => Int -> Int -> v a -> V.Vector (v a)
linToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VG.slice (i*w) w lvec)

IL(mLinToMat) :: (VGM.MVector v a) => Int -> Int -> v s a -> V.Vector (v s a)
mLinToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VGM.slice (i*w) w lvec)

IL(unsafeAddrToSVec) :: Int -> Addr# -> VS.Vector Word8
unsafeAddrToSVec n addr
  = (`VS.unsafeFromForeignPtr0` n)
    $ unsafeDupablePerformIO
    $ newForeignPtr_ $ Ptr addr

IL(vEvalElemsId) :: (VG.Vector v a) => v a -> v a
vEvalElemsId = vMapFoldl (\ !_ !x -> (x,())) ()

IL(vEvalElems) :: (VG.Vector v a) => v a -> ()
vEvalElems = VG.foldl' (\ !_ !_ -> ()) ()

IL(vMapFoldl) :: (VG.Vector v b, VG.Vector v c) =>
  (a -> b -> (c,a)) -> a -> v b -> v c
vMapFoldl f a
  = VG.unstream . VFB.inplace (streamMapFoldl f a) id . VG.stream

streamMapFoldl :: (Functor m) =>
  (a -> b -> (c,a)) -> a -> VFSM.Stream m b -> VFSM.Stream m c
{-# INLINE_FUSED streamMapFoldl #-}
streamMapFoldl f a (VFSM.Stream step s) = VFSM.Stream step1 (a,s)
  where
    {-# INLINE_INNER step1 #-}
    step1 (a0,s0) =  (<$> step s0) $ \r -> case r of
      VFSM.Yield b s1 -> case f a0 b of (c,a1) -> VFSM.Yield c (a1,s1)
      VFSM.Skip    s1 -> VFSM.Skip (a0,s1)
      VFSM.Done       -> VFSM.Done

IL(svecToBS) :: VS.Vector Word8 -> BS.ByteString
svecToBS vec = BSU.fromForeignPtr ptr 0 len
  where (ptr, len) = VS.unsafeToForeignPtr0 vec

unlessM, whenM :: (Monad m) => m Bool -> m () -> m ()
IL(whenM) = (. flip when) . (>>=)
IL(unlessM) = (. flip unless) . (>>=)

IL(wrA) = A.writeArray
IL(rdA) = A.readArray
IL(mdA) = \arr f !i -> do
  ai <- rdA arr i
  let fai = f ai
  wrA arr i fai
  return (ai,fai)
{-# INLINE mdA' #-}
mdA' = \arr f !i -> do
  !ai <- rdA arr i
  let !fai = f ai
  wrA arr i fai
  return (ai,fai)
IL(swapA) = \arr !i !j -> do
  ai <- rdA arr i
  wrA arr i =<< rdA arr j
  wrA arr j ai

#define D(f,r,d)\
  IL(f) :: Integral a=>a->d; f=fromIntegral;\
  IL(r) :: String->d; r=read
#define C(f,r,g,h,d) D(f,r,d);\
  g,h :: RealFrac a=>a->d; IL(g)=floor; IL(h)=ceiling
C(_toInteger_,readInteger,floorInteger,ceilInteger,Integer)
C(toInt,readInt,floorInt,ceilInt,Int)
C(toI8,readI8,floorI8,ceilI8,Int8)
C(toI16,readI16,floorI16,ceilI16,Int16)
C(toI32,readI32,floorI32,ceilI32,Int32)
C(toI64,readI64,floorI64,ceilI64,Int64)
C(toWord,readWord,floorWord,ceilWord,Word)
C(toW8,readW8,floorW8,ceilW8,Word8)
C(toW16,readW16,floorW16,ceilW16,Word16)
C(toW32,readW32,floorW32,ceilW32,Word32)
C(toW64,readW64,floorW64,ceilW64,Word64)
D(toDouble,readDouble,Double)
D(toFloat,readFloat,Float)
#undef D
#undef C

#define TS(f,a,m,init)\
  IL(f) :: forall e i s. (C(a,m) A.Ix i) => (i,i) -> init m (a i e); f
#define N(f,g,h,a,m)\
  TS(f,a,m,e->)=A.newArray;\
  TS(g,a,m,)=A.newArray_;\
  TS(h,a,m,[e]->)=A.newListArray
#define C(a,m)
N(newIOA,newIOA_,newIOAL,IOArray,IO)
N(newSTA,newSTA_,newSTAL,STArray s,ST s)
#undef C
#define C(a,m) MArray (a) e (m),
N(newIOUA,newIOUA_,newIOUAL,IOUArray,IO)
N(newSTUA,newSTUA_,newSTUAL,STUArray s,ST s)
#undef C
#undef N
#undef TS

#undef IL

Score : 200 points

Problem Statement

We have N squares assigned the numbers 1,2,3,\ldots,N. Each square has an integer written on it, and the integer written on Square i is a_i.

How many squares i satisfy both of the following conditions?

The assigned number, i, is odd.

The written integer is odd.

Constraints

All values in input are integers.

1 \leq N, a_i \leq 100

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \cdots a_N

Output

Print the number of squares that satisfy both of the conditions.

Sample Input 1

5
1 3 4 5 7

Sample Output 1

2

Two squares, Square 1 and 5, satisfy both of the conditions.

For Square 2 and 4, the assigned numbers are not odd.

For Square 3, the written integer is not odd.

Sample Input 2

15
13 76 46 15 50 98 93 77 31 43 84 90 6 24 14

Sample Output 2

3


import Data.Array
import Data.Bits
import qualified Data.ByteString.Char8 as BS
import Data.List
import Data.Maybe
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt = fst . fromJust . BS.readInt

getInt = readInt <$> BS.getLine

getVU n = VU.reverse . VU.unfoldrN n BS.uncons <$> BS.getLine

simulate :: Integer -> Integer -> Integer
simulate count 0 = count
simulate count x = simulate (count + 1) (x `mod` (fromIntegral (popCount x)))

solve :: Int -> Integer -> Int -> Integer -> Integer -> Integer -> Integer -> Integer
solve b x n p0 p1 s0 s1 = do
  let x' = complementBit x b
  if x' == 0
    then 0
    else do
      let b' = testBit x' (fromIntegral b)
      let d = if b' then (2 ^ (fromIntegral b) `mod` p0 + s0) `mod` p0 else (- 2 ^ (fromIntegral b) `mod` p1 + s1) `mod` p1
      simulate 1 d

createBits :: VU.Vector Char -> Integer
createBits = VU.ifoldl' (\bit index value -> if value == '1' then setBit bit index else bit) zeroBits

main = do
  n <- getInt
  x <- getVU n
  let x' = createBits x
  let ppc = fromIntegral (popCount x')
  let p0 = ppc + 1
  let p1 = ppc - 1
  let s0 = x' `mod` p0
  let s1 = x' `mod` p1
  let bs = reverse [0 .. (fromIntegral n -1)]
  let x'' = map (\b -> solve b x' n p0 p1 s0 s1) bs
  mapM_ print x''

Score : 400 points

Problem Statement

Let \mathrm{popcount}(n) be the number of 1s in the binary representation of n.
For example, \mathrm{popcount}(3) = 2, \mathrm{popcount}(7) = 3, and \mathrm{popcount}(0) = 0.

Let f(n) be the number of times the following operation will be done when we repeat it until n becomes 0: "replace n with the remainder when n is divided by \mathrm{popcount}(n)." (It can be proved that, under the constraints of this problem, n always becomes 0 after a finite number of operations.)

For example, when n=7, it becomes 0 after two operations, as follows:

\mathrm{popcount}(7)=3, so we divide 7 by 3 and replace it with the remainder, 1.

\mathrm{popcount}(1)=1, so we divide 1 by 1 and replace it with the remainder, 0.

You are given an integer X with N digits in binary.
For each integer i such that 1 \leq i \leq N, let X_i be what X becomes when the i-th bit from the top is inverted.
Find f(X_1), f(X_2), \ldots, f(X_N).

Constraints

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

X is an integer with N digits in binary, possibly with leading zeros.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print N lines. The i-th line should contain the value f(X_i).

Sample Input 1

3
011

Sample Output 1

2
1
1

X_1 = 7, which will change as follows: 7 \rightarrow 1 \rightarrow 0. Thus, f(7) = 2.

X_2 = 1, which will change as follows: 1 \rightarrow 0. Thus, f(1) = 1.

X_3 = 2, which will change as follows: 2 \rightarrow 0. Thus, f(2) = 1.

Sample Input 2

23
00110111001011011001110

Sample Output 2

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


{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.Reader
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bifunctor
import           Data.Bool
import qualified Data.ByteString               as B
import qualified Data.ByteString.Builder       as B
import qualified Data.ByteString.Char8         as C
import qualified Data.ByteString.Internal      as B
import qualified Data.ByteString.Unsafe        as B
import           Data.Char
import qualified Data.Foldable                 as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntSet                   as IS
import qualified Data.List                     as L
import qualified Data.Map.Strict               as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Proxy
import           Data.Ratio
import           Data.Semigroup hiding (diff)
import qualified Data.Set                      as S
import           Data.Tuple
import qualified Data.Vector                   as V
import qualified Data.Vector.Generic           as G
import qualified Data.Vector.Generic.Mutable   as GM
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Primitive         as P
import qualified Data.Vector.Primitive.Mutable as PM
import qualified Data.Vector.Unboxed           as U
import qualified Data.Vector.Unboxed.Mutable   as UM
import           Debug.Trace
import           Foreign                       hiding (void)
import           GHC.Exts
import           GHC.TypeLits
import qualified System.IO                     as IO
import           Unsafe.Coerce
import System.Exit

main :: IO ()
main = do
    n <- readLn :: IO Int
    xs <- U.unfoldrN n (runParser $ digitToInt <$> char) <$> C.getContents
    B.hPutBuilder IO.stdout . U.foldr (\x acc -> B.intDec x <> B.char7 '\n' <> acc) mempty
        $ solve n xs

diff :: Int -> Int
diff 1 = -1
diff 0 = 1
diff _ = 0

solve :: Int -> U.Vector Int -> U.Vector Int
solve n xs = U.generate n $ \i ->
        let cmp = complementBit nat (n - 1 - i)
            -- cnt = count + diff (xs U.! i)
        in 1 + table U.! fromIntegral (cmp `mod` fromIntegral (popCount cmp))
  where
    nat :: Integer
    !nat = U.foldl' (\acc d -> 2 * acc + fromIntegral d) 0 xs
    count :: Int
    !count = U.length $ U.filter (== 1) xs
    table :: U.Vector Int
    !table = U.generate 1000000 (length.simulate)

simulate :: Int -> [Int]
simulate x = takeWhile (/=0) $ iterate step x
  where
    step 0 = 0
    step i = rem i (popCount i)

-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: Monad m => Int -> (Int -> m ()) -> m ()
rep !n = U.forM_ $ U.generate n id
{-# INLINE rep #-}
rev :: Monad m => Int -> (Int -> m ()) -> m ()
rev !n = U.forM_ $ U.iterateN n (subtract 1) (n - 1)
{-# INLINE rev #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}


module Main where

count :: Eq a => a -> [a] -> Int
count _ [] = 0
count a (x:xs)
	| a == x = 1 + count a xs
	| otherwise = count a xs

summary :: [String] -> String
summary results = "AC x " ++ ac ++ "\nWA x " ++ wa ++ "\nTLE x " ++ tle ++ "\nRE x " ++ re
	where { ac = show $ count "AC" results ;
		wa = show $ count "WA" results ;
		tle = show $ count "TLE" results ;
		re = show $ count "RE" results }

main :: IO ()
main = interact $ summary . tail . lines

Score : 200 points

Problem Statement

Takahashi is participating in a programming contest called AXC002, and he has just submitted his code to Problem A.

The problem has N test cases.

For each test case i (1\leq i \leq N), you are given a string S_i representing the verdict for that test case. Find the numbers of test cases for which the verdict is AC, WA, TLE, and RE, respectively.

See the Output section for the output format.

Constraints

1 \leq N \leq 10^5

S_i is AC, WA, TLE, or RE.

Input

Input is given from Standard Input in the following format:

N
S_1
\vdots
S_N

Output

Let C_0, C_1, C_2, and C_3 be the numbers of test cases for which the verdict is AC, WA, TLE, and RE, respectively. Print the following:

AC x C_0
WA x C_1
TLE x C_2
RE x C_3

Sample Input 1

6
AC
TLE
AC
AC
WA
TLE

Sample Output 1

AC x 3
WA x 1
TLE x 2
RE x 0

We have 3, 1, 2, and 0 test case(s) for which the verdict is AC, WA, TLE, and RE, respectively.

Sample Input 2

10
AC
AC
AC
AC
AC
AC
AC
AC
AC
AC

Sample Output 2

AC x 10
WA x 0
TLE x 0
RE x 0


main :: IO ()
main = do
  sn <- getContents

  let s = lines sn
  let ac = length $ filter (== "AC") s
  let wa = length $ filter (== "WA") s
  let tle = length $ filter (== "TLE") s
  let re = length $ filter (== "RE") s

  putStr "AC x "
  print ac
  putStr "WA x "
  print wa
  putStr "TLE x "
  print tle
  putStr "RE x "
  print re


import Data.List
import Data.Maybe

main = do
    n <- getLine >>= return . read
    ss <- mapM (\_ -> getLine) [1..n]
    let g = map (\x -> (head x, length x)) $ group $ sort ss
    putStrLn ("AC x " ++ show (a "AC" g))
    putStrLn ("WA x " ++ show (a "WA" g))
    putStrLn ("TLE x " ++ show (a "TLE" g))
    putStrLn ("RE x " ++ show (a "RE" g))

a code g = if isJust c then snd (fromJust c) else 0
    where
        c = b code g

b code g = find (\x -> (fst x) == code ) g


{-# LANGUAGE MultiWayIf #-}

module Main where
import           Prelude
import           Control.Monad
import           Data.Monoid
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Vector                   as V
import           Data.Vector.Algorithms.Search
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM
import           Debug.Trace
--import qualified Data.Heap                     as H
import qualified Data.Sequence                 as SQ
import qualified Data.Graph.Inductive.PatriciaTree
                                               as G
import qualified Data.Graph.Inductive.Graph    as G
import           Data.Int
import           Data.Bits

main = do
  --aN       <- getI
  --[aA, aB] <- getIL
  --aS       <- getLine
  aN  <- getI
  aSA <- replicateM aN $ do
    aS <- getLine
    if
      | aS == "AC"  -> return (0, 1) :: IO (Int, Int)
      | aS == "WA"  -> return (1, 1)
      | aS == "TLE" -> return (2, 1)
      | aS == "RE"  -> return (3, 1)
      | otherwise   -> return (4, 1)

  let ans = VU.accum (+) (VU.replicate 5 0) aSA

  putStrLn $ "AC x " ++ (show $ans VU.! 0)
  putStrLn $ "WA x " ++ (show $ans VU.! 1)
  putStrLn $ "TLE x " ++ (show $ans VU.! 2)
  putStrLn $ "RE x " ++ (show $ans VU.! 3)

  return ()
{-
hMaxPoint :: Int
hMaxPoint = 101
hMaximum :: H.Heap Int -> Int
hMaximum h = hMaxPoint - (H.minimum h)
hInsertMax :: Int -> H.Heap Int -> H.Heap Int
hInsertMax x = H.insert (hMaxPoint - x)
hDeleteMax :: H.Heap Int -> H.Heap Int
hDeleteMax = H.deleteMin
-}

{-
aroundSquare y x h w =
  [ aYX
  | aYX@(aY, aX) <- [(y - 1, x), (y, x - 1), (y + 1, x), (y, x + 1), (y, x)]
  , aY >= 0
  , aY <= (h - 1)
  , aX >= 0
  , aX <= (w - 1)
  ]
-}

splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs =
  let (bs1, newBs) = BSC8.splitAt 1 bs
  in  if newBs == BSC8.empty
        then [test $ BSC8.readInt bs1]
        else (test $ BSC8.readInt bs1) : (splitReadBSC8 newBs)
  where test (Just (i, _)) = i

read2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> IO Char
read2DimChar vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x
write2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> Char -> IO ()
write2DimChar vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

readTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> IO Int
readTwoDimVec vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x
writeTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> Int -> IO ()
writeTwoDimVec vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine

getRepVUI :: Int -> IO (VU.Vector Int)
getRepVUI n =
  VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace)
    .   BSC8.unlines
    <$> replicateM n BSC8.getLine

getVS :: IO (V.Vector Char)
getVS = V.fromList <$> getLine

getVUC :: IO (VU.Vector Char)
getVUC = VU.fromList <$> getLine

readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt

readIL :: BSC8.ByteString -> [Int]
readIL = map readI . BSC8.words

readIT2 :: BSC8.ByteString -> (Int, Int)
readIT2 bs =
  let words = BSC8.words bs in (readI $ head words, readI $ last words)

getI :: IO Int
getI = readI <$> BSC8.getLine

getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine

getIT2 :: IO (Int, Int)
getIT2 = readIT2 <$> BSC8.getLine

getIT2Order :: IO (Int, Int)
getIT2Order =
  getIL >>= \x@[xz, xo] -> if xz > xo then return (xo, xz) else return (xz, xo)

getNIS :: Int -> IO [(Int, BSC8.ByteString)]
getNIS 0 = return []
getNIS n = do
  [aFst, aSnd] <- BSC8.words <$> BSC8.getLine
  next         <- getNIS (n - 1)
  return ((readI aFst, aSnd) : next)

il2Words :: [Int] -> String
il2Words = unwords . map show

il2Lines :: [Int] -> String
il2Lines = unlines . map show

p :: Int -> Int
p x = x - 1

--modNum = 10 ^ 9 + 7
--modulus = 1000000007
modulus = 2019

newtype MInt = M Int

instance Num MInt where
  (M a) + (M b) = M $ mod (a + b) modulus

  (M a) - (M b) = M $ mod (a - b) modulus

  (M a) * (M b) = M $ mod (a * b) modulus

  fromInteger a = M $ mod (fromInteger a) modulus

  abs (M a) = M $ abs a

  signum (M a) = M $ signum a

instance Show MInt where
  show (M a) = show (mod a modulus)

int2MInt :: Int -> MInt
int2MInt a = M (mod a modulus)

mInt2Int :: MInt -> Int
mInt2Int (M a) = a

{-
factsMod :: V.Vector MInt
factsMod = V.scanl (\acc x -> M x * acc) 1 $ V.generate 2000000 (+ 1)

factMod :: Int -> MInt
factMod = (factsMod V.!)
-}

factMod :: Int -> MInt
factMod n | n == 0    = 1
          | n == 1    = 1
          | otherwise = M n * (factMod (n - 1))

factDivMod :: Int -> Int -> MInt
factDivMod n k | n == k    = M 1
               | otherwise = M n * (factDivMod (n - 1) k)

powMod :: MInt -> MInt -> MInt
powMod n mK@(M k) | k == 0       = M 1
                  | k == 1       = n
                  | mod k 2 == 0 = powMod (n ^ 2) (M (div k 2))
                  | otherwise    = n * powMod (n ^ 2) (M (div k 2))

invMod :: MInt -> MInt
invMod (M 0) = error "inverse of 0"
invMod x     = powMod x (M (modulus - 2))

{-
combiMod :: Int -> Int -> MInt
combiMod n k
  | n < 0 || k < 0 || k > n = 0
  | otherwise = factMod n * invMod (factMod (n - k)) * invMod (factMod k)
-}
combiMod :: Int -> Int -> MInt
combiMod n k | n < 0 || k < 0 || k > n = 0
             | k > n - k = factDivMod n k * invMod (factMod (n - k))
             | otherwise = factDivMod n (n - k) * invMod (factMod k)

combi :: Int -> Int -> Int
combi n k | n < 0 || k < 0 || k > n = 0
          | k == n                  = 1
          | otherwise               = div (div (fact n) (fact (n - k))) (fact k)

{-w
primes :: Integral a => [a]
primes = map fromIntegral $ [2, 3] ++ primes'
 where
  primes' = [5] ++ f 1 7 primes'
  f m s (p : ps) = [ n | n <- ns, gcd m n == 1 ] ++ f (m * p) (p * p) ps
    where ns = [ x + y | x <- [s, s + 6 .. p * p - 2], y <- [0, 4] ]

prime n = primes !! n
primes = sieve [2 ..]
sieve (p : xs) = p : sieve [ x | x <- xs, x `mod` p /= 0 ]
-}
fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsackWDP :: Int -> [(Int, Int)] -> VU.Vector Int
knappsackWDP maxW [] = VU.replicate (maxW + 1) 0
knappsackWDP maxW ((w, v) : xs) =
  let tailDP = knappsackWDP maxW xs
  in  VU.generate (maxW + 1) $ \i -> if w <= i
        then max (tailDP VU.! i) (tailDP VU.! (i - w) + v)
        else tailDP VU.! i

knappsackVDP :: Int -> Int -> Int -> [(Int, Int)] -> VU.Vector Int
knappsackVDP maxW maxV n [] = VU.cons 0 $ VU.replicate (n * maxV) maxW
knappsackVDP maxW maxV n ((w, v) : xs) =
  let tailDP = knappsackVDP maxW maxV n xs
  in  VU.generate (n * maxV + 1) $ \i -> if v <= i
        then min (tailDP VU.! i) (tailDP VU.! (i - v) + w)
        else tailDP VU.! i

knappsackMinVol
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> Int
  -> IO Int
knappsackMinVol dp volumeVec valueVec dpSize maxVolume = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if (v + value) > dpSize
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v + value)
            dpIV  <- AIO.readArray dp (i, v)
            return (min (dpIVm - volume) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      (reverse [0 .. dpSize])
    )
    [0 .. VU.length valueVec - 1]
  foldM
    (\acc x -> do
      num <- AIO.readArray dp (VU.length volumeVec, x)
      return $ if num <= maxVolume then x else acc
    )
    0
    [0 .. dpSize]

lcsTable :: BS.ByteString -> BS.ByteString -> V.Vector (VU.Vector Int)
lcsTable xs ys = V.scanl step (VU.replicate (m + 1) 0) xs'
 where
  n   = BS.length xs
  m   = BS.length ys
  xs' = V.generate n $ BSC8.index xs :: V.Vector Char
  ys' = VU.generate m $ BSC8.index ys :: VU.Vector Char
  step :: VU.Vector Int -> Char -> VU.Vector Int
  step v x = VU.scanl innerStep 0 (VU.zip3 v (VU.tail v) ys')
   where
    innerStep :: Int -> (Int, Int, Char) -> Int
    innerStep a (b, c, y) | x == y    = 1 + b
                          | otherwise = max a c
{-
main = do
xs <- BS.getLine
ys <- BS.getLine
print $ VU.last $ V.last $ lcsTable xs ys
-}

myFilter :: (a -> Bool) -> [a] -> ([a], [a])
myFilter _pred [] = ([], [])
myFilter pred (x : xs)
  | pred x    = let (l, r) = myFilter pred xs in (x : l, r)
  | otherwise = let (l, r) = myFilter pred xs in (l, x : r)

--UnionFindデータ構造
type UF_PARENT = VUM.IOVector Int
type UF_RANK = VUM.IOVector Int
type UF = (UF_PARENT, UF_RANK)
uf_makeSet :: Int -> IO UF
uf_makeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank   <- VUM.replicate n 0
  return (parent, rank)
uf_union :: UF -> Int -> Int -> IO ()
uf_union unionFind@(parents, ranks) x y = do
  xRoot     <- uf_find unionFind x
  yRoot     <- uf_find unionFind y
  xRootRank <- VUM.read ranks xRoot
  yRootRank <- VUM.read ranks yRoot
  if
    | xRootRank > yRootRank -> VUM.write parents yRoot xRoot
    | xRootRank < yRootRank -> VUM.write parents xRoot yRoot
    | xRoot /= yRoot -> do
      VUM.write parents yRoot xRoot
      VUM.write ranks xRoot (xRootRank + 1)
    | otherwise -> return ()

uf_find :: UF -> Int -> IO Int
uf_find unionFind@(parents, ranks) x = do
  xParent <- VUM.read parents x
  if xParent == x
    then return x
    else do
      xRootParent <- uf_find unionFind xParent
      VUM.write parents x xRootParent
      return xRootParent

--UnDirectedGraph(無向グラフ)データ構造
type UDG = M.Map Int [Int]
list2UDG :: [(Int, Int)] -> M.Map Int [Int]
list2UDG = foldl
  (\acc x ->
    let lr = M.insertWith (++) (fst x) [snd x] acc
    in  M.insertWith (++) (snd x) [fst x] lr
  )
  M.empty


import Data.List

main=do
    n <- getLine
    xs <- words <$> getLine
    print $ ans (read n :: Int) (sort (map (read::String -> Int) xs))

ans n xs = sum $ take (n-1) (kurik 0 (reverse xs))

kurik x xs = (xs !! div (x+1) 2):(kurik (x+1) xs)

Score: 400 points

Problem Statement

Quickly after finishing the tutorial of the online game ATChat, you have decided to visit a particular place with N-1 players who happen to be there. These N players, including you, are numbered 1 through N, and the friendliness of Player i is A_i.

The N players will arrive at the place one by one in some order. To make sure nobody gets lost, you have set the following rule: players who have already arrived there should form a circle, and a player who has just arrived there should cut into the circle somewhere.

When each player, except the first one to arrive, arrives at the place, the player gets comfort equal to the smaller of the friendliness of the clockwise adjacent player and that of the counter-clockwise adjacent player. The first player to arrive there gets the comfort of 0.

What is the maximum total comfort the N players can get by optimally choosing the order of arrivals and the positions in the circle to cut into?

Constraints

All values in input are integers.

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

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the maximum total comfort the N players can get.

Sample Input 1

4
2 2 1 3

Sample Output 1

7

By arriving at the place in the order Player 4, 2, 1, 3, and cutting into the circle as shown in the figure, they can get the total comfort of 7.

They cannot get the total comfort greater than 7, so the answer is 7.

Sample Input 2

7
1 1 1 1 1 1 1

Sample Output 2

6


import Control.Monad
import qualified Data.ByteString.Char8 as BS
import Data.Function
import Data.List
import Data.Maybe
import Data.Ord
import qualified Data.Vector as V
import qualified Data.Vector.Algorithms.Intro as VAIT
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt = fst . fromJust . BS.readInt

readInteger = fst . fromJust . BS.readInteger

readIntList = map readInt . BS.words

readIntegerList = map readInteger . BS.words

getIntList = readIntList <$> BS.getLine

getIntegerList = readIntegerList <$> BS.getLine

prod :: VU.Vector Int -> Int
prod = VU.foldl1' (\x y -> x * y `mod` (10^9+7))

sortVecOn :: (Ord a, VG.Vector v b) => (b -> a) -> v b -> v b
sortVecOn f vec = VG.create $ do
  vec <- VG.thaw vec
  VAIT.sortBy (compare `on` f) vec
  return vec

mod1G7 :: Integer -> Int
mod1G7 n = fromIntegral (n `mod` (10 ^ 9 + 7))

main :: IO ()
main = do
  [n, k] <- getIntList
  as <- getIntList
  let as' = VU.fromList as
  if k == n
    then print $ prod as'
    else do
      if VU.all (<= 0) as'
        then
          if odd k
            then print $ prod $ VU.take k $ sortVecOn Down as'
            else print $ prod $ VU.take k $ sortVecOn id as'
        else do
          let as'' = sortVecOn (\a -> (- (abs a))) as'
          let bs = VU.take k as''
          let s = prod bs
          if s > 0
            then print s
            else do
              let bsr = VU.reverse bs
              let cs = VU.drop k as''
              let bs' = VU.filter (\b' -> b' < 0) bsr
              let cs' = VU.filter (\a -> a > 0) cs
              let d = if VU.length cs' == 0 || VU.length bs' == 0 then 0 else s `div` (fromIntegral (VU.head bs')) * (fromIntegral (VU.head cs'))
              let bs'' = VU.filter (\b' -> b' > 0) bsr
              let cs'' = VU.filter (\a -> a < 0) cs
              let d' = if VU.length cs'' == 0 || VU.length bs'' == 0 then 0 else s `div` (fromIntegral (VU.head bs'')) * (fromIntegral (VU.head cs''))
              if d == 0 && d' == 0
                then print $ prod (VU.take k (VU.filter (\a -> a <= 0) (VU.reverse as')))
                else print $ mod1G7 (maximum [(fromIntegral d), (fromIntegral d')])

Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

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

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).


{-# LANGUAGE
  ScopedTypeVariables, BangPatterns, TupleSections, ExplicitForAll,
  LambdaCase, MultiWayIf, Unsafe, RecordWildCards, FlexibleContexts, CPP,
  NoMonomorphismRestriction, GADTs, PatternGuards, MagicHash, UnboxedTuples,
  RankNTypes, EmptyDataDecls, EmptyCase, ViewPatterns, PolyKinds,
  TypeFamilies, OverloadedStrings, FlexibleInstances, UndecidableInstances,
  DefaultSignatures, GeneralizedNewtypeDeriving, StandaloneDeriving,
  DeriveGeneric, DeriveFunctor, DeriveDataTypeable, DeriveFoldable,
  DeriveTraversable, DeriveDataTypeable, FlexibleInstances,
  MultiParamTypeClasses, TypeApplications, RecordWildCards,
  NumericUnderscores #-}
{-# OPTIONS_GHC -O2 #-}

#define PHASE_FUSED [1]
#define PHASE_INNER [0]
#define INLINE_FUSED INLINE PHASE_FUSED
#define INLINE_INNER INLINE PHASE_INNER

import Prelude
import Data.Bits
import Data.List
import Data.Maybe
import Data.Tuple
import Data.Ord
import Data.Int
import Data.Word
import Data.Char
import Data.Ratio
import Data.Function
import Data.STRef
import Data.IORef
import Data.Monoid
import Data.Functor
import Data.Functor.Identity
import Data.Data
import Data.Typeable
import GHC.Generics
import System.IO
import System.IO.Unsafe (unsafeDupablePerformIO, unsafePerformIO)
import Control.Arrow
import Control.Applicative
import Control.Monad
import Control.Monad.Primitive
import Control.Monad.State.Strict
import Control.Monad.ST
import Control.Monad.ST.Lazy (strictToLazyST, lazyToStrictST)
import qualified Control.Monad.ST.Lazy as STL
-- import Control.Monad.ST.Safe
import Control.DeepSeq
import Data.Coerce
import qualified Data.ByteString as BSW
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy as BSLW
import qualified Data.ByteString.Lazy.Char8 as BSL
import qualified Data.ByteString.Builder as BSB
import qualified Data.ByteString.Unsafe as BSU
import qualified Data.ByteString.Internal as BSU
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IMS
import qualified Data.IntMap.Lazy as IML
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Storable as VS
import qualified Data.Vector.Storable.Mutable as VSM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Vector.Fusion.Bundle.Monadic as VFBM
import qualified Data.Vector.Fusion.Bundle as VFB
import qualified Data.Vector.Fusion.Stream.Monadic as VFSM
import qualified Data.Vector.Fusion.Bundle.Size as VFBS
import qualified Data.Vector.Fusion.Util as VFU
import qualified Data.Vector.Algorithms.Intro as VAIT
import qualified Data.Attoparsec.ByteString.Char8 as Atto
import Debug.Trace
import Unsafe.Coerce
import Foreign.ForeignPtr
import GHC.Exts (build, Int(..), Int#,
                 (+#), (*#), (-#), (<#), (>=#), (==#), quotRemInt#,
                 remInt#, uncheckedIShiftRL#, andI#, orI#,
                isTrue#, Addr#, Ptr(..))

main :: IO ()
main = do
  [n,k] <- map readInt . words <$> getLine
  as <- getVecULn n rIntS
  print
    $ if VU.all (<=0) as
      then
        if even k
        then prod $ VU.take k $ sortVecOn id as
        else prod $ VU.take k $ sortVecOn Down as
      else
        let (xs,ys) = runST $ do
              as_ <- VU.unsafeThaw as
              VAIT.selectBy (compare `on` (Down . abs)) as_ k
              VAIT.sortBy (compare `on` abs) (VUM.take k as_)
              VAIT.sortBy (compare `on` (Down . abs)) (VUM.drop k as_)
              (,)
                 <$> VU.unsafeFreeze (VUM.take k as_)
                 <*> VU.unsafeFreeze (VUM.drop k as_)
            cnt = VFB.length $ VG.stream $ VU.filter (<0) xs
            prd = prod xs
        in if | even cnt -> prd
              | VU.any (==0) xs -> remF 0
              | otherwise ->
                let posBig = VU.find (>0) xs
                    negBig = VU.find (<0) xs
                    posLittle = VU.find (>=0) ys
                    negLittle = VU.find (<=0) ys
                in case (liftA2 (,) posBig negLittle,
                         liftA2 (,) negBig posLittle)
                   of (Nothing,Nothing) -> undefined
                      (Just (posBig,negLittle),Nothing)
                        -> prd / fromIntegral posBig * fromIntegral negLittle
                      (Nothing, Just (negBig, posLittle))
                        -> prd / fromIntegral negBig * fromIntegral posLittle
                      (Just (posBig,negLittle), Just (negBig,posLittle))
                        | negLittle * negBig > posLittle * posBig ->
                          prd / fromIntegral posBig * fromIntegral negLittle
                        | otherwise ->
                          prd / fromIntegral negBig * fromIntegral posLittle
  return ()

prod :: VU.Vector Int -> RemF
prod = VU.product . VU.map fromIntegral

sortVecOn :: (Ord a, VG.Vector v b) =>
  (b -> a) -> v b -> v b
{-# INLINE sortVecOn #-}
sortVecOn f vec = VG.create $ do
  vec <- VG.thaw vec
  VAIT.sortBy (compare `on` f) vec
  return vec

data FixedModulus

instance HasWord32 FixedModulus where
  {-# INLINE CONLIKE word32Val #-}
  word32Val = const 1000000007 -- 10^9 + 7

type RemF = Rem FixedModulus

pxyF :: Proxy FixedModulus
pxyF = Proxy
remF :: Word32 -> RemF
{-# INLINE CONLIKE remF #-}
remF = Rem

newtype Magic r = Magic (forall (m :: *). HasWord32 m => Proxy m -> r)

{-# INLINE reifyWord32 #-}
reifyWord32 :: forall a. Word32 ->
  (forall (m :: *). HasWord32 m => Proxy m -> a) -> a
reifyWord32 v f = unsafeCoerce (Magic f :: Magic a) (const v) Proxy

newtype Rem m = Rem {unRem :: Word32} deriving (Eq)

withTypeArgOf :: c a -> d a -> c a
{-# INLINE CONLIKE withTypeArgOf #-}
withTypeArgOf = const

proxyFor :: c a -> Proxy a
{-# INLINE CONLIKE proxyFor #-}
proxyFor = const Proxy

withProxy :: (Proxy m -> c m) -> c m
{-# INLINE withProxy #-}
withProxy f = f Proxy

remP :: Proxy m -> Word32 -> Rem m
{-# INLINE CONLIKE remP #-}
remP = const Rem

{-# INLINE modulus32 #-}
modulus32 :: HasWord32 m => Rem m -> Word32
modulus32 x = word32Val $ proxyFor x

class HasWord32 m where
  word32Val :: Proxy m -> Word32

instance Show (Rem m) where
  {-# INLINE showsPrec #-}
  showsPrec = coerce `asTypeOf` (\f p (Rem v) -> f p v) $ showsPrec

negRem :: HasWord32 m => Rem m -> Rem m
{-# INLINE negRem #-}
negRem x0@(Rem x)
  | x == 0 = Rem 0
  | otherwise = Rem $ modulus32 x0 - x

addRem, subRem, multRem
  :: HasWord32 m => Rem m -> Rem m -> Rem m
{-# INLINE subRem #-}
subRem x0@(Rem x) (Rem y) = Rem $ x-y + if x < y then modulus32 x0 else 0
{-# INLINE addRem #-}
addRem x0@(Rem x) (Rem y) = Rem $ x-negy + if x < negy then m else 0
  where m = modulus32 x0; negy = m-y
{-# INLINE multRem #-}
multRem x0@(Rem x) (Rem y)
  = Rem $ toW32 $ (toW64 x * toW64 y) `rem` toW64 (modulus32 x0)

{-# INLINE fromIntegerRem #-}
fromIntegerRem :: (HasWord32 m) => Integer -> Rem m
fromIntegerRem x = withProxy $ Rem . fromInteger . mod x . toInteger . word32Val

{-# INLINE signumRem #-}
signumRem :: (HasWord32 m) => Rem m -> Rem m
signumRem = (\case True -> Rem 0; False -> Rem 1) . (== Rem 0)

instance HasWord32 m => Num (Rem m) where
  {-# INLINE negate #-}
  negate = negRem
  {-# INLINE (-) #-}
  (-) = subRem
  {-# INLINE (+) #-}
  (+) = addRem
  {-# INLINE (*) #-}
  (*) = multRem
  {-# INLINE fromInteger #-}
  fromInteger = fromIntegerRem
  {-# INLINE abs #-}
  abs = id
  {-# INLINE signum #-}
  signum = signumRem

recipRem :: HasWord32 m => Rem m -> Rem m
{-# INLINE recipRem #-}
recipRem = \x -> x ^ (modulus32 x - 2)

-- works only for primes
instance HasWord32 m => Fractional (Rem m) where
  {-# INLINE recip #-}
  recip = recipRem
  fromRational q = fromInteger (numerator q) / fromInteger (denominator q)

newtype instance VU.Vector (Rem m)
  = VRem { unVRem :: VU.Vector Word32 }
newtype instance VUM.MVector s (Rem m)
  = VMRem { unVMRem :: VUM.MVector s Word32 }
instance VUM.Unbox (Rem m)

instance VGM.MVector VUM.MVector (Rem m) where
  {-# INLINE basicLength #-}
  basicLength = coerce `asTypeOf` (. unVMRem) $ VGM.basicLength
  {-# INLINE basicUnsafeSlice #-}
  basicUnsafeSlice
    = coerce `asTypeOf` (\f x y (VMRem v) -> VMRem $ f x y v)
      $ VGM.basicUnsafeSlice
  {-# INLINE basicOverlaps #-}
  basicOverlaps = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicOverlaps
  {-# INLINE basicUnsafeNew #-}
  basicUnsafeNew = fmap (coerce `asTypeOf` VMRem) . VGM.basicUnsafeNew
  {-# INLINE basicInitialize #-}
  basicInitialize = coerce `asTypeOf` (. unVMRem) $ VGM.basicInitialize
  {-# INLINE basicUnsafeReplicate #-}
  basicUnsafeReplicate !n
    = fmap (coerce `asTypeOf` VMRem) . VGM.basicUnsafeReplicate n
    . unRem
  {-# INLINE basicUnsafeRead #-}
  basicUnsafeRead (VMRem v) i = coerce `asTypeOf` Rem <$>
                                VGM.basicUnsafeRead v i
  {-# INLINE basicUnsafeWrite #-}
  basicUnsafeWrite = coerce `asTypeOf` (\f (VMRem v) n (Rem x) -> f v n x)
                     $ VGM.basicUnsafeWrite
  {-# INLINE basicClear #-}
  basicClear = coerce `asTypeOf` (. unVMRem) $ VGM.basicClear
  {-# INLINE basicSet #-}
  basicSet = coerce `asTypeOf` (\f (VMRem v) (Rem x) -> f v x) $ VGM.basicSet
  {-# INLINE basicUnsafeCopy #-}
  basicUnsafeCopy = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicUnsafeCopy
  {-# INLINE basicUnsafeMove #-}
  basicUnsafeMove = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicUnsafeMove
  {-# INLINE basicUnsafeGrow #-}
  basicUnsafeGrow (VMRem v) !n
    = fmap (coerce `asTypeOf` VMRem) $ VGM.basicUnsafeGrow v n

instance VG.Vector VU.Vector (Rem m) where
  {-# INLINE basicUnsafeFreeze #-}
  basicUnsafeFreeze (VMRem v)
    = (coerce `asTypeOf` VRem) <$> VG.basicUnsafeFreeze v
  {-# INLINE basicUnsafeThaw #-}
  basicUnsafeThaw (VRem v)
    = (coerce `asTypeOf` VMRem) <$> VG.basicUnsafeThaw v
  {-# INLINE basicLength #-}
  basicLength = coerce `asTypeOf` (. unVRem) $ VG.basicLength
  {-# INLINE basicUnsafeSlice #-}
  basicUnsafeSlice
    = coerce `asTypeOf` (\f i l (VRem v) -> VRem $ f i l v)
      $ VG.basicUnsafeSlice
  {-# INLINE basicUnsafeIndexM #-}
  basicUnsafeIndexM (VRem !v) !i = coerce <$> VG.basicUnsafeIndexM v i
  {-# INLINE basicUnsafeCopy #-}
  basicUnsafeCopy
    = coerce `asTypeOf` (\f (VMRem mv) (VRem v) -> f mv v)
      $ VG.basicUnsafeCopy
  {-# INLINE elemseq #-}
  elemseq = const seq

#define IL(f) {-# INLINE f #-}; f

IL(putBuilder) = BSB.hPutBuilder stdout

printVecInLines, printVecInSpcSepLn ::
  (VG.Vector v a, ShowAsBuilder a) => v a -> IO ()
IL(printVecInLines) = putBuilder . v2BLines
IL(printVecInSpcSepLn) = putBuilder . v2BSpcSepLn

class ShowAsBuilder a where
  showAsBuilder :: a -> BSB.Builder
  default showAsBuilder :: (Show a) => a -> BSB.Builder
  IL(showAsBuilder) = BSB.string8 . show

-- Inconsistent with show
instance (ShowAsBuilder a, VG.Vector v a) => ShowAsBuilder (v a) where
  IL(showAsBuilder) = v2BSpcSep

#define INS(t,f) instance ShowAsBuilder t where { IL(showAsBuilder)=f }
INS(Int,BSB.intDec)
INS(Int8,BSB.int8Dec)
INS(Int16,BSB.int16Dec)
INS(Int32,BSB.int32Dec)
INS(Int64,BSB.int64Dec)
INS(Word,BSB.wordDec)
INS(Word8,BSB.word8Dec)
INS(Word16,BSB.word16Dec)
INS(Word32,BSB.word32Dec)
INS(Word64,BSB.word64Dec)
INS(Integer,BSB.integerDec)
INS(Float,BSB.floatDec)
INS(Double,BSB.doubleDec)
-- INS(String,BSB.string8) -- Inconsistent with Show
-- INS(BS.ByteString,BSB.byteString) -- Inconsistent with Show
-- INS(BSL.ByteString,BSB.lazyByteString) -- Inconsisitent with Show
#undef INS

-- Inconsistent with Show
instance (ShowAsBuilder a, ShowAsBuilder b) => ShowAsBuilder (a,b) where
  IL(showAsBuilder) = showTupAsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c) =>
  ShowAsBuilder (a,b,c) where
  IL(showAsBuilder) = showTup3AsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  ShowAsBuilder (a,b,c,d) where
  IL(showAsBuilder) = showTup4AsBuilder

IL(showTupAsBuilderWith)
  :: (a -> BSB.Builder) -> (b -> BSB.Builder) -> (a,b) -> BSB.Builder
showTupAsBuilderWith showA showB
  = \(a,b) -> (showA a <>) $ BSB.char7 ' ' <> showB b
IL(showTupAsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b)
  => (a,b) -> BSB.Builder
showTupAsBuilder = showTupAsBuilderWith showAsBuilder showAsBuilder

IL(showTup3AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (a,b,c) -> BSB.Builder
showTup3AsBuilderWith showA showB showC
  = \(a,b,c) -> (showA a <>) $ (BSB.char7 ' ' <>) $ (showB b <>)
                $ (BSB.char7 ' ' <>) $ showC c
IL(showTup3AsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c)
  => (a,b,c) -> BSB.Builder
showTup3AsBuilder
  = showTup3AsBuilderWith showAsBuilder showAsBuilder showAsBuilder

IL(showTup4AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (d -> BSB.Builder) -> (a,b,c,d) -> BSB.Builder
showTup4AsBuilderWith showA showB showC showD
  = \(a,b,c,d) -> (showA a <>) $ (BSB.char7 ' ' <>)
                  $ showTup3AsBuilderWith showB showC showD (b,c,d)
IL(showTup4AsBuilder) ::
  (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  (a,b,c,d) -> BSB.Builder
showTup4AsBuilder = showTup4AsBuilderWith showAsBuilder showAsBuilder
                    showAsBuilder showAsBuilder

v2BSpcSepLn, v2BSpcSep, v2BConcat, v2BLines ::
  (VG.Vector v a, ShowAsBuilder a)
  => v a -> BSB.Builder
IL(v2BSpcSepLn) = v2BSpcSepLnWith showAsBuilder
IL(v2BSpcSep) = v2BSpcSepWith showAsBuilder
IL(v2BConcat) = v2BConcatWith showAsBuilder
IL(v2BLines) = v2BLinesWith showAsBuilder

v2BSpcSepLnWith, v2BSpcSepWith, v2BConcatWith, v2BLinesWith ::
  (VG.Vector v a)
  => (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepLnWith) = v2BSpcSepPostfWith $ BS.singleton '\n'
IL(v2BSpcSepWith) = v2BSpcSepPostfWith BS.empty
IL(v2BConcatWith) showFct = VG.foldr ((<>) . showFct) mempty
IL(v2BLinesWith) showFct
  = VG.foldr (\ a -> (showFct a <>) . (BSB.char7 '\n' <>)) mempty

v2BSpcSepPostf :: (VG.Vector v a, ShowAsBuilder a)
  => BS.ByteString -- ^ postfix
  -> v a -> BSB.Builder
IL(v2BSpcSepPostf) = (`v2BSpcSepPostfWith` showAsBuilder)

v2BSpcSepPostfWith :: (VG.Vector v a)
  => BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepPostfWith) = vecToBuilder BS.empty $ BS.singleton ' '

IL(vecToBuilder) :: (VG.Vector v a)
  => BS.ByteString -- ^ prefix
  -> BS.ByteString -- ^ separator
  -> BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder !prefix !separator !postfix
  = vecToBuilder_ (BSB.byteString prefix)
                  (BSB.byteString separator)
                  (BSB.byteString postfix)

IL(vecToBuilder_) :: (VG.Vector v a)
  => BSB.Builder -- ^ prefix
  -> BSB.Builder -- ^ separator
  -> BSB.Builder -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder_ !prefix !separator !postfix showFct = \vec -> prefix <>
  VG.foldr
  (\ a rest !prefx -> prefx <> (showFct a <> rest separator))
  (const postfix) vec mempty

IL(evalVals) :: [a] -> [a]
evalVals xs = build $ \c n -> foldr (c $!) n xs
IL(forceVals) :: (NFData a) => [a] -> [a]
forceVals xs = build $ \c n -> foldr (c $!!) n xs

IL(readLnWith) :: StateT BS.ByteString Maybe a -> IO a
readLnWith parser = fromJust . evalStateT parser <$> BS.getLine
IL(readContentWith) :: StateT BSL.ByteString Maybe a -> IO a
readContentWith parser = fromJust . evalStateT parser <$> BSL.getContents

IL(getVecGLn) :: (VG.Vector v a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (v a)
getVecGLn n s = VG.unfoldrN n (runStateT s) <$> BS.getLine
IL(getVecGRest) :: (VG.Vector v a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (v a)
getVecGRest n s = VG.unfoldrN n (runStateT s) <$> BSL.getContents
IL(getVecLn) :: Int -> StateT BS.ByteString Maybe a -> IO (V.Vector a)
getVecLn = getVecGLn
IL(getVecRest) :: Int -> StateT BSL.ByteString Maybe a -> IO (V.Vector a)
getVecRest = getVecGRest
IL(getVecULn) :: (VU.Unbox a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (VU.Vector a)
getVecULn = getVecGLn
IL(getVecURest) :: (VU.Unbox a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (VU.Vector a)
getVecURest = getVecGRest

IL(rIntL) :: StateT BSL.ByteString Maybe Int
rIntL = skipSpecialL $ StateT BSL.readInt
IL(rIntS) :: StateT BS.ByteString Maybe Int
rIntS = skipSpecialS $ StateT BS.readInt
IL(rStrL) :: (MonadState BSL.ByteString m) => m BS.ByteString
rStrL = skipSpecialL $ BSL.toStrict <$> state (BSL.span (>='!'))
IL(rStrS) :: (MonadState BS.ByteString m) => m BS.ByteString
rStrS = skipSpecialS $ state $ BS.span (>='!')
IL(rCharL) :: StateT BSL.ByteString Maybe Char
rCharL = StateT BSL.uncons
IL(rCharS) :: StateT BS.ByteString Maybe Char
rCharS = StateT BS.uncons
IL(rCharWL) :: StateT BSL.ByteString Maybe Word8
rCharWL = StateT BSLW.uncons
IL(rCharWS) :: StateT BS.ByteString Maybe Word8
rCharWS = StateT BSW.uncons
IL(dropSpecialL) :: (MonadState BSL.ByteString m) => m ()
dropSpecialL = modify $ BSL.dropWhile (<'!')
IL(dropSpecialS) :: (MonadState BS.ByteString m) => m ()
dropSpecialS = modify $ BS.dropWhile (<'!')
IL(skipSpecialL) :: (MonadState BSL.ByteString m) => m a -> m a
skipSpecialL = (dropSpecialL *>)
IL(skipSpecialS) :: (MonadState BS.ByteString m) => m a -> m a
skipSpecialS = (dropSpecialS *>)

IL(linToMat) :: (VG.Vector v a) => Int -> Int -> v a -> V.Vector (v a)
linToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VG.slice (i*w) w lvec)

IL(mLinToMat) :: (VGM.MVector v a) => Int -> Int -> v s a -> V.Vector (v s a)
mLinToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VGM.slice (i*w) w lvec)

IL(unsafeAddrToSVec) :: Int -> Addr# -> VS.Vector Word8
unsafeAddrToSVec n addr
  = (`VS.unsafeFromForeignPtr0` n)
    $ unsafeDupablePerformIO
    $ newForeignPtr_ $ Ptr addr

IL(vEvalElemsId) :: (VG.Vector v a) => v a -> v a
vEvalElemsId = vMapFoldl (\ !_ !x -> (x,())) ()

IL(vEvalElems) :: (VG.Vector v a) => v a -> ()
vEvalElems = VG.foldl' (\ !_ !_ -> ()) ()

IL(vMapFoldl) :: (VG.Vector v b, VG.Vector v c) =>
  (a -> b -> (c,a)) -> a -> v b -> v c
vMapFoldl f a
  = VG.unstream . VFB.inplace (streamMapFoldl f a) id . VG.stream

streamMapFoldl :: (Functor m) =>
  (a -> b -> (c,a)) -> a -> VFSM.Stream m b -> VFSM.Stream m c
{-# INLINE_FUSED streamMapFoldl #-}
streamMapFoldl f a (VFSM.Stream step s) = VFSM.Stream step1 (a,s)
  where
    {-# INLINE_INNER step1 #-}
    step1 (a0,s0) =  (<$> step s0) $ \r -> case r of
      VFSM.Yield b s1 -> case f a0 b of (c,a1) -> VFSM.Yield c (a1,s1)
      VFSM.Skip    s1 -> VFSM.Skip (a0,s1)
      VFSM.Done       -> VFSM.Done

IL(svecToBS) :: VS.Vector Word8 -> BS.ByteString
svecToBS vec = BSU.fromForeignPtr ptr 0 len
  where (ptr, len) = VS.unsafeToForeignPtr0 vec

unlessM, whenM :: (Monad m) => m Bool -> m () -> m ()
IL(whenM) = (. flip when) . (>>=)
IL(unlessM) = (. flip unless) . (>>=)

IL(wrA) = A.writeArray
IL(rdA) = A.readArray
IL(mdA) = \arr f !i -> do
  ai <- rdA arr i
  let fai = f ai
  wrA arr i fai
  return (ai,fai)
{-# INLINE mdA' #-}
mdA' = \arr f !i -> do
  !ai <- rdA arr i
  let !fai = f ai
  wrA arr i fai
  return (ai,fai)
IL(swapA) = \arr !i !j -> do
  ai <- rdA arr i
  wrA arr i =<< rdA arr j
  wrA arr j ai

#define D(f,r,d)\
  IL(f) :: Integral a=>a->d; f=fromIntegral;\
  IL(r) :: String->d; r=read
#define C(f,r,g,h,d) D(f,r,d);\
  g,h :: RealFrac a=>a->d; IL(g)=floor; IL(h)=ceiling
C(_toInteger_,readInteger,floorInteger,ceilInteger,Integer)
C(toInt,readInt,floorInt,ceilInt,Int)
C(toI8,readI8,floorI8,ceilI8,Int8)
C(toI16,readI16,floorI16,ceilI16,Int16)
C(toI32,readI32,floorI32,ceilI32,Int32)
C(toI64,readI64,floorI64,ceilI64,Int64)
C(toWord,readWord,floorWord,ceilWord,Word)
C(toW8,readW8,floorW8,ceilW8,Word8)
C(toW16,readW16,floorW16,ceilW16,Word16)
C(toW32,readW32,floorW32,ceilW32,Word32)
C(toW64,readW64,floorW64,ceilW64,Word64)
D(toDouble,readDouble,Double)
D(toFloat,readFloat,Float)
#undef D
#undef C

#define TS(f,a,m,init)\
  IL(f) :: forall e i s. (C(a,m) A.Ix i) => (i,i) -> init m (a i e); f
#define N(f,g,h,a,m)\
  TS(f,a,m,e->)=A.newArray;\
  TS(g,a,m,)=A.newArray_;\
  TS(h,a,m,[e]->)=A.newListArray
#define C(a,m)
N(newIOA,newIOA_,newIOAL,IOArray,IO)
N(newSTA,newSTA_,newSTAL,STArray s,ST s)
#undef C
#define C(a,m) MArray (a) e (m),
N(newIOUA,newIOUA_,newIOUAL,IOUArray,IO)
N(newSTUA,newSTUA_,newSTUAL,STUArray s,ST s)
#undef C
#undef N
#undef TS

#undef IL


import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    a <- getInt
    print $ a + (a^2) + (a^3)

Score : 100 points

Problem Statement

Given an integer a as input, print the value a + a^2 + a^3.

Constraints

1 \leq a \leq 10

a is an integer.

Input

Input is given from Standard Input in the following format:

a

Output

Print the value a + a^2 + a^3 as an integer.

Sample Input 1

2

Sample Output 1

14

When a = 2, we have a + a^2 + a^3 = 2 + 2^2 + 2^3 = 2 + 4 + 8 = 14.

Print the answer as an input. Outputs such as 14.0 will be judged as incorrect.

Sample Input 2

10

Sample Output 2

1110


import Data.Char

main :: IO ()
main = do
    c <- getChar
    putStrLn $ if isUpper c then "A" else "a"

Score : 100 points

Problem Statement

An uppercase or lowercase English letter \alpha will be given as input.
If \alpha is uppercase, print A; if it is lowercase, print a.

Constraints

\alpha is an uppercase (A - Z) or lowercase (a - z) English letter.

Input

Input is given from Standard Input in the following format:

α

Output

If \alpha is uppercase, print A; if it is lowercase, print a.

Sample Input 1

B

Sample Output 1

A

B is uppercase, so we should print A.

Sample Input 2

a

Sample Output 2

a

a is lowercase, so we should print a.


import Control.Arrow (second)
import Data.List (sort, scanl1)
import Data.Vector.Unboxed (Vector)
import qualified Data.Vector.Unboxed as UV
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as BSC8

main :: IO ()
main = do
  let readInt = fmap (second BSC8.tail) . BSC8.readInt
  (n, k) <- (\vec -> (vec UV.! 0, vec UV.! 1)) . UV.unfoldrN 2 readInt <$> BSC8.getLine

  ps <- UV.unfoldrN n readInt <$> BSC8.getLine
  print $ sum $ take k $ sort $ UV.toList ps

Score : 200 points

Problem Statement

A shop sells N kinds of fruits, Fruit 1, \ldots, N, at prices of p_1, \ldots, p_N yen per item, respectively. (Yen is the currency of Japan.)

Here, we will choose K kinds of fruits and buy one of each chosen kind. Find the minimum possible total price of those fruits.

Constraints

1 \leq K \leq N \leq 1000

1 \leq p_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
p_1 p_2 \ldots p_N

Output

Print an integer representing the minimum possible total price of fruits.

Sample Input 1

5 3
50 100 80 120 80

Sample Output 1

210

This shop sells Fruit 1, 2, 3, 4, and 5 for 50 yen, 100 yen, 80 yen, 120 yen, and 80 yen, respectively.

The minimum total price for three kinds of fruits is 50 + 80 + 80 = 210 yen when choosing Fruit 1, 3, and 5.

Sample Input 2

1 1
1000

Sample Output 2

1000


{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE BinaryLiterals #-}
{-# LANGUAGE BangPatterns #-}

-- Default Imports

import Control.Monad
import Control.Monad.ST
import Control.Monad.Trans.Class

import qualified Control.Monad.Reader as Reader
import Control.Monad.Reader (Reader, ReaderT, runReader, runReaderT)

import qualified Data.Array.MArray as MArray
import qualified Data.Array.ST as STArray
import Data.Array.ST (STArray, STUArray, runSTArray, runSTUArray)
import Data.Ix (Ix)

import qualified Data.Bits as Bits
import Data.Bits ((.&.), (.|.))

import qualified Data.ByteString.Char8 as BS
import Data.ByteString.Char8 (ByteString)

import qualified Data.Char as Char
import qualified Data.List as List
import qualified Data.Map.Strict as Map
import Data.Map.Strict (Map)
import qualified Data.Maybe as Maybe
import qualified Data.Set as Set
import Data.Set (Set)

import qualified Data.Vector as Vector
import qualified Data.Vector.Generic as GVector
import qualified Data.Vector.Mutable as MVector
import Data.Vector.Mutable (STVector)
import qualified Data.Vector.Unboxed as UVector

import Numeric

import Debug.Trace
-- ----------

-- Custom Import Here

-- ----------

-- Default Definitions

type Vector = Vector.Vector
-- type GVector = GVector.Vector
type UVector = UVector.Vector

readIntToList :: ByteString -> [Int]
readIntToList = List.unfoldr (fmap (second $ BS.dropWhile Char.isSpace) . BS.readInt)

readToList :: Read a => ByteString -> [a]
readToList = List.unfoldr $ fmap (mapTaken . mapRemain) . span' (not . Char.isSpace)
	where
		mapTaken  = first $ read . BS.unpack
		mapRemain = second $ BS.dropWhile Char.isSpace
		span' pred s
			| BS.null taken = Nothing
			| otherwise     = Just (taken, remain')
			where
				(taken, remain) = BS.span pred s
				remain' = BS.dropWhile Char.isSpace remain

readToListN :: Read a => Int -> ByteString -> [a]
readToListN n = take n . readToList

readIntToVector :: ByteString -> Vector Int
readIntToVector = Vector.unfoldr (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

readIntToUVector :: ByteString -> UVector.Vector Int
readIntToUVector = UVector.unfoldr (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

readIntToVectorN :: Int -> ByteString -> Vector.Vector Int
readIntToVectorN n = Vector.unfoldrN n (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

readIntToUVectorN :: Int -> ByteString -> UVector.Vector Int
readIntToUVectorN n = UVector.unfoldrN n (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

first :: (a -> a') -> (a, b) -> (a', b)
first f (a, b) = (f a, b)

second :: (b -> b') -> (a, b) -> (a, b')
second f (a, b) = (a, f b)

average :: Fractional a => [a] -> a
average xs = sum xs / (fromIntegral . length) xs

-- ----------

main :: IO ()
main = do
	[n, k] <- readIntToList <$> BS.getLine
	ps <- readIntToList <$> BS.getLine
	print $ sum $ take k $ List.sort ps


main=readLn>>=putStrLn.reverse.f
f 0=""
f n=(toEnum(97+c)::Char):f m
 where (m,c)=divMod(n-1)26

Score : 300 points

Problem Statement

1000000000000001 dogs suddenly appeared under the roof of Roger's house, all of which he decided to keep. The dogs had been numbered 1 through 1000000000000001, but he gave them new names, as follows:

the dogs numbered 1,2,\cdots,26 were respectively given the names a, b, ..., z;

the dogs numbered 27,28,29,\cdots,701,702 were respectively given the names aa, ab, ac, ..., zy, zz;

the dogs numbered 703,704,705,\cdots,18277,18278 were respectively given the names aaa, aab, aac, ..., zzy, zzz;

the dogs numbered 18279,18280,18281,\cdots,475253,475254 were respectively given the names aaaa, aaab, aaac, ..., zzzy, zzzz;

the dogs numbered 475255,475256,\cdots were respectively given the names aaaaa, aaaab, ...;

and so on.

To sum it up, the dogs numbered 1, 2, \cdots were respectively given the following names:

a, b, ..., z, aa, ab, ..., az, ba, bb, ..., bz, ..., za, zb, ..., zz, aaa, aab, ..., aaz, aba, abb, ..., abz, ..., zzz, aaaa, ...

Now, Roger asks you:

"What is the name for the dog numbered N?"

Constraints

N is an integer.

1 \leq N \leq 1000000000000001

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer to Roger's question as a string consisting of lowercase English letters.

Sample Input 1

2

Sample Output 1

b

Sample Input 2

27

Sample Output 2

aa

Sample Input 3

123456789

Sample Output 3

jjddja


import Data.Char

main :: IO ()
main = do
    n <- readLn
    let res = stack n []
    putStrLn res
        where
            numToChar n = chr $ n + (ord 'a') - 1
            stack n xs
                | n == 0 = xs
                | n <= 26 = (numToChar n) : xs
                | otherwise =
                    let q = (n - 1) `div` 26
                        r = n `mod` 26
                        c = numToChar $ if r == 0 then 26 else r
                    in  stack q (c : xs)


main = solve . head . map read . words <$> getLine >>= putStrLn

cs = ['a'..'z']

at 0 (c:_) = c
at n (_:l) = at (n-1) l

solve n = reverse $ solve' (n-1)

solve' :: Integer -> String
solve' n
    | n < 26   = [at n' cs]
    | otherwise = at n' cs : solve' n''
    where
        n'  = n `mod` 26
        n'' = n `div` 26 - 1


main = solve . head . map read . words <$> getLine >>= print

cs = ['a'..'z']

at 1 (c:_) = c
at n (_:l) = at (n-1) l
at _ []    = '_'

solve n = reverse $ solve' n

solve' :: Integer -> String
solve' n
    | n <= 26    = [at n cs]
    | otherwise = at n' cs : solve' n''
    where
        n'  = n `mod` 26
        n'' = n `div` 26


import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Data.Char
import Data.IORef
import Data.List
import Data.Maybe

main = do
  n <- getInt
  as <- getIntVec n
  v <- MV.replicate (10^5+1) 0 :: IO (MV.IOVector Int)
  s <- newIORef 0
  V.forM_ as $ \i -> do
    modifyIORef s (+i)
    MV.modify v (+1) i
  q <- getInt
  replicateM_ q $ do
    (b, c) <- getIntPair
    m <- MV.read v b
    modifyIORef s (+ ((c - b) * m))
    MV.write v b 0
    MV.modify v (+m) c
    print =<< readIORef s

getInt :: IO Int
getInt = readLn

second :: (b -> c) -> (a, b) -> (a, c)
second f (a, b) = (a, f b)

readInt :: BS.ByteString -> Maybe (Int, BS.ByteString)
readInt = fmap (second BS.tail) . BS.readInt

getIntVec :: Int -> IO (V.Vector Int)
getIntVec n = V.unfoldrN n readInt <$> BS.getLine

getIntList :: IO [Int]
getIntList = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

getIntPair :: IO (Int, Int)
getIntPair = do
  v <- getIntVec 2
  return (v V.! 0, v V.! 1)

Score : 400 points

Problem Statement

You have a sequence A composed of N positive integers: A_{1}, A_{2}, \cdots, A_{N}.

You will now successively do the following Q operations:

In the i-th operation, you replace every element whose value is B_{i} with C_{i}.

For each i (1 \leq i \leq Q), find S_{i}: the sum of all elements in A just after the i-th operation.

Constraints

All values in input are integers.

1 \leq N, Q, A_{i}, B_{i}, C_{i} \leq 10^{5}

B_{i} \neq C_{i}

Input

Input is given from Standard Input in the following format:

N
A_{1} A_{2} \cdots A_{N}
Q
B_{1} C_{1}
B_{2} C_{2}
\vdots
B_{Q} C_{Q}

Output

Print Q integers S_{i} to Standard Output in the following format:

S_{1}
S_{2}
\vdots
S_{Q}

Note that S_{i} may not fit into a 32-bit integer.

Sample Input 1

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

Sample Output 1

11
12
16

Initially, the sequence A is 1,2,3,4.

After each operation, it becomes the following:

2, 2, 3, 4

2, 2, 4, 4

4, 4, 4, 4

Sample Input 2

4
1 1 1 1
3
1 2
2 1
3 5

Sample Output 2

8
4
4

Note that the sequence A may not contain an element whose value is B_{i}.

Sample Input 3

2
1 2
3
1 100
2 100
100 1000

Sample Output 3

102
200
2000


{-# LANGUAGE MultiWayIf #-}

module Main where
import           Prelude
import           Control.Monad
import           Data.Monoid
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Vector                   as V
--import           Data.Vector.Algorithms.Search
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM
import           Debug.Trace
--import qualified Data.Heap                     as H
import qualified Data.Sequence                 as SQ
import qualified Data.Graph.Inductive.PatriciaTree
                                               as G
import qualified Data.Graph.Inductive.Graph    as G
import           Data.Int
import           Data.Bits

main = do
  --aN       <- getI
  --[aA, aB] <- getIL
  --aS       <- getLine

  aN  <- getI
  aA  <- getIL
  aQ  <- getI
  aBC <- replicateM aQ getIT2

  let accumList = map (\a -> (a, 1 :: Int)) aA
  let initedAcc = VU.accum (+) (VU.replicate (10 ^ 5 + 1) 0) accumList

  let sumNum =
        sum $ map (\x -> initedAcc VU.! x * x) [0 .. VU.length initedAcc - 1]

  let
    accumedList = scanl
      (\acc@(acch, accm, accs) (f, s) ->
        let
          target  = if S.member f acch then 0 else initedAcc VU.! f
          aaa     = M.findWithDefault 0 f accm
          newaccm = M.insertWith (-) f (target + aaa)
            $ M.insertWith (+) s (target + aaa) accm
          newacch = S.insert f acch
        in
          (newacch, newaccm, (accs - (target + aaa) * f + (target + aaa) * s))
      )
      (S.empty, M.empty, sumNum)
      (aBC :: [(Int, Int)])

  mapM_ (\(h, m, n) -> print n) $tail accumedList

  return ()

getName n =
  let ndiv26 = div n 26
      nmod26 = mod n 26
  in  if ndiv26 >= 1 then nmod26 : getName ndiv26 else [nmod26]

{-
hMaxPoint :: Int
hMaxPoint = 101
hMaximum :: H.Heap Int -> Int
hMaximum h = hMaxPoint - (H.minimum h)
hInsertMax :: Int -> H.Heap Int -> H.Heap Int
hInsertMax x = H.insert (hMaxPoint - x)
hDeleteMax :: H.Heap Int -> H.Heap Int
hDeleteMax = H.deleteMin
-}

{-
aroundSquare y x h w =
  [ aYX
  | aYX@(aY, aX) <- [(y - 1, x), (y, x - 1), (y + 1, x), (y, x + 1), (y, x)]
  , aY >= 0
  , aY <= (h - 1)
  , aX >= 0
  , aX <= (w - 1)
  ]
-}

splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs =
  let (bs1, newBs) = BSC8.splitAt 1 bs
  in  if newBs == BSC8.empty
        then [test $ BSC8.readInt bs1]
        else (test $ BSC8.readInt bs1) : (splitReadBSC8 newBs)
  where test (Just (i, _)) = i

read2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> IO Char
read2DimChar vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x
write2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> Char -> IO ()
write2DimChar vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

readTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> IO Int
readTwoDimVec vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x
writeTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> Int -> IO ()
writeTwoDimVec vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine

getRepVUI :: Int -> IO (VU.Vector Int)
getRepVUI n =
  VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace)
    .   BSC8.unlines
    <$> replicateM n BSC8.getLine

getVS :: IO (V.Vector Char)
getVS = V.fromList <$> getLine

getVUC :: IO (VU.Vector Char)
getVUC = VU.fromList <$> getLine

readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt

readIL :: BSC8.ByteString -> [Int]
readIL = map readI . BSC8.words

readIT2 :: BSC8.ByteString -> (Int, Int)
readIT2 bs =
  let words = BSC8.words bs in (readI $ head words, readI $ last words)

getI :: IO Int
getI = readI <$> BSC8.getLine

getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine

getIT2 :: IO (Int, Int)
getIT2 = readIT2 <$> BSC8.getLine

getIT2Order :: IO (Int, Int)
getIT2Order =
  getIL >>= \x@[xz, xo] -> if xz > xo then return (xo, xz) else return (xz, xo)

getNIS :: Int -> IO [(Int, BSC8.ByteString)]
getNIS 0 = return []
getNIS n = do
  [aFst, aSnd] <- BSC8.words <$> BSC8.getLine
  next         <- getNIS (n - 1)
  return ((readI aFst, aSnd) : next)

il2Words :: [Int] -> String
il2Words = unwords . map show

il2Lines :: [Int] -> String
il2Lines = unlines . map show

p :: Int -> Int
p x = x - 1

--modNum = 10 ^ 9 + 7
--modulus = 1000000007
modulus = 2019

newtype MInt = M Int

instance Num MInt where
  (M a) + (M b) = M $ mod (a + b) modulus

  (M a) - (M b) = M $ mod (a - b) modulus

  (M a) * (M b) = M $ mod (a * b) modulus

  fromInteger a = M $ mod (fromInteger a) modulus

  abs (M a) = M $ abs a

  signum (M a) = M $ signum a

instance Show MInt where
  show (M a) = show (mod a modulus)

int2MInt :: Int -> MInt
int2MInt a = M (mod a modulus)

mInt2Int :: MInt -> Int
mInt2Int (M a) = a

{-
factsMod :: V.Vector MInt
factsMod = V.scanl (\acc x -> M x * acc) 1 $ V.generate 2000000 (+ 1)

factMod :: Int -> MInt
factMod = (factsMod V.!)
-}

factMod :: Int -> MInt
factMod n | n == 0    = 1
          | n == 1    = 1
          | otherwise = M n * (factMod (n - 1))

factDivMod :: Int -> Int -> MInt
factDivMod n k | n == k    = M 1
               | otherwise = M n * (factDivMod (n - 1) k)

powMod :: MInt -> MInt -> MInt
powMod n mK@(M k) | k == 0       = M 1
                  | k == 1       = n
                  | mod k 2 == 0 = powMod (n ^ 2) (M (div k 2))
                  | otherwise    = n * powMod (n ^ 2) (M (div k 2))

invMod :: MInt -> MInt
invMod (M 0) = error "inverse of 0"
invMod x     = powMod x (M (modulus - 2))

{-
combiMod :: Int -> Int -> MInt
combiMod n k
  | n < 0 || k < 0 || k > n = 0
  | otherwise = factMod n * invMod (factMod (n - k)) * invMod (factMod k)
-}
combiMod :: Int -> Int -> MInt
combiMod n k | n < 0 || k < 0 || k > n = 0
             | k > n - k = factDivMod n k * invMod (factMod (n - k))
             | otherwise = factDivMod n (n - k) * invMod (factMod k)

combi :: Int -> Int -> Int
combi n k | n < 0 || k < 0 || k > n = 0
          | k == n                  = 1
          | otherwise               = div (div (fact n) (fact (n - k))) (fact k)

{-w
primes :: Integral a => [a]
primes = map fromIntegral $ [2, 3] ++ primes'
 where
  primes' = [5] ++ f 1 7 primes'
  f m s (p : ps) = [ n | n <- ns, gcd m n == 1 ] ++ f (m * p) (p * p) ps
    where ns = [ x + y | x <- [s, s + 6 .. p * p - 2], y <- [0, 4] ]

prime n = primes !! n
primes = sieve [2 ..]
sieve (p : xs) = p : sieve [ x | x <- xs, x `mod` p /= 0 ]
-}
fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsackWDP :: Int -> [(Int, Int)] -> VU.Vector Int
knappsackWDP maxW [] = VU.replicate (maxW + 1) 0
knappsackWDP maxW ((w, v) : xs) =
  let tailDP = knappsackWDP maxW xs
  in  VU.generate (maxW + 1) $ \i -> if w <= i
        then max (tailDP VU.! i) (tailDP VU.! (i - w) + v)
        else tailDP VU.! i

knappsackVDP :: Int -> Int -> Int -> [(Int, Int)] -> VU.Vector Int
knappsackVDP maxW maxV n [] = VU.cons 0 $ VU.replicate (n * maxV) maxW
knappsackVDP maxW maxV n ((w, v) : xs) =
  let tailDP = knappsackVDP maxW maxV n xs
  in  VU.generate (n * maxV + 1) $ \i -> if v <= i
        then min (tailDP VU.! i) (tailDP VU.! (i - v) + w)
        else tailDP VU.! i

knappsackMinVol
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> Int
  -> IO Int
knappsackMinVol dp volumeVec valueVec dpSize maxVolume = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if (v + value) > dpSize
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v + value)
            dpIV  <- AIO.readArray dp (i, v)
            return (min (dpIVm - volume) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      (reverse [0 .. dpSize])
    )
    [0 .. VU.length valueVec - 1]
  foldM
    (\acc x -> do
      num <- AIO.readArray dp (VU.length volumeVec, x)
      return $ if num <= maxVolume then x else acc
    )
    0
    [0 .. dpSize]

lcsTable :: BS.ByteString -> BS.ByteString -> V.Vector (VU.Vector Int)
lcsTable xs ys = V.scanl step (VU.replicate (m + 1) 0) xs'
 where
  n   = BS.length xs
  m   = BS.length ys
  xs' = V.generate n $ BSC8.index xs :: V.Vector Char
  ys' = VU.generate m $ BSC8.index ys :: VU.Vector Char
  step :: VU.Vector Int -> Char -> VU.Vector Int
  step v x = VU.scanl innerStep 0 (VU.zip3 v (VU.tail v) ys')
   where
    innerStep :: Int -> (Int, Int, Char) -> Int
    innerStep a (b, c, y) | x == y    = 1 + b
                          | otherwise = max a c
{-
main = do
xs <- BS.getLine
ys <- BS.getLine
print $ VU.last $ V.last $ lcsTable xs ys
-}

myFilter :: (a -> Bool) -> [a] -> ([a], [a])
myFilter _pred [] = ([], [])
myFilter pred (x : xs)
  | pred x    = let (l, r) = myFilter pred xs in (x : l, r)
  | otherwise = let (l, r) = myFilter pred xs in (l, x : r)

--UnionFindデータ構造
type UF_PARENT = VUM.IOVector Int
type UF_RANK = VUM.IOVector Int
type UF = (UF_PARENT, UF_RANK)
uf_makeSet :: Int -> IO UF
uf_makeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank   <- VUM.replicate n 0
  return (parent, rank)
uf_union :: UF -> Int -> Int -> IO ()
uf_union unionFind@(parents, ranks) x y = do
  xRoot     <- uf_find unionFind x
  yRoot     <- uf_find unionFind y
  xRootRank <- VUM.read ranks xRoot
  yRootRank <- VUM.read ranks yRoot
  if
    | xRootRank > yRootRank -> VUM.write parents yRoot xRoot
    | xRootRank < yRootRank -> VUM.write parents xRoot yRoot
    | xRoot /= yRoot -> do
      VUM.write parents yRoot xRoot
      VUM.write ranks xRoot (xRootRank + 1)
    | otherwise -> return ()

uf_find :: UF -> Int -> IO Int
uf_find unionFind@(parents, ranks) x = do
  xParent <- VUM.read parents x
  if xParent == x
    then return x
    else do
      xRootParent <- uf_find unionFind xParent
      VUM.write parents x xRootParent
      return xRootParent

--UnDirectedGraph(無向グラフ)データ構造
type UDG = M.Map Int [Int]
list2UDG :: [(Int, Int)] -> M.Map Int [Int]
list2UDG = foldl
  (\acc x ->
    let lr = M.insertWith (++) (fst x) [snd x] acc
    in  M.insertWith (++) (snd x) [fst x] lr
  )
  M.empty


solve :: Int -> Int -> String
solve x y =
    let ok = not . null . filter f $ [(c, t) | c <- [0..50], t <- [0..25]]
    in if ok then "Yes" else "No"
        where f (c, t) = c + t == x && 2*c + 4*t == y

main :: IO ()
main = do
    [x, y] <- map read . words <$> getLine
    putStrLn $ solve x y

Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.


{-# LANGUAGE BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import qualified Data.Map.Strict             as Map
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector                 as VB
import qualified Data.Vector.Mutable         as VBM
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

inf :: Int
inf = 10^18

main = do
  [x, y] <- getIntList

  let solve i | i > x     = "No"
              | otherwise = let j = x - i
                                n = i * 2 + j * 4
                            in if n == y
                               then "Yes"
                               else solve (i+1)

  putStrLn $ solve 0


import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    [x,y] <- getIntList
    let b2 = y - 2 * x
    let a = x - b2 `div` 2
    putStrLn $ if b2 >= 0 && a >= 0 && b2 `mod` 2 == 0 then "Yes" else "No"