Problem:
Score : 200 points

Problem Statement

Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:

Red boxes, each containing R red balls

Green boxes, each containing G green balls

Blue boxes, each containing B blue balls

Snuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.
How many triples of non-negative integers (r,g,b) achieve this?

Constraints

All values in input are integers.

1 \leq R,G,B,N \leq 3000

Input

Input is given from Standard Input in the following format:

R G B N

Output

Print the answer.

Sample Input 1

1 2 3 4

Sample Output 1

4

Four triples achieve the objective, as follows:

(4,0,0)

(2,1,0)

(1,0,1)

(0,2,0)

Sample Input 2

13 1 4 3000

Sample Output 2

87058

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

module Main where

import Data.List
import Control.Monad
import Debug.Trace
import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust, catMaybes)
import qualified Data.Vector as V


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = do
    strs <- BC.words  <$> BC.getLine
    let bcList = catMaybes $ (BC.readInt <$> strs)
    pure $ fst <$> bcList

onOffLists :: Int -> Int -> [[Int]]
onOffLists i m = if i == m then [[0], [1]] else
    let
        prevLists = onOffLists (i + 1) m
    in
        [(1:), (0:)] <*> prevLists

checkVector :: [([Int], Int)] -> V.Vector Int -> Bool
checkVector ss v = all checker ss where
    checker (s,p) = ((foldr (\si acc -> (v V.! (si - 1) ) + acc ) 0 s) `mod` 2) == p

main = do
    [r, g, b, n] <- readInts
    let maxR =  n `div` r
    let ans = foldr (\rNum acc ->
            acc + foldr (\gNum acc -> 
                if (n - rNum * r - gNum * g) `mod` b == 0 then 1 + acc else 0 + acc
                ) 0 [0..(n - rNum * r) `div` g]
            ) 0 [0..maxR]
    print ans