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)

{-# LANGUAGE ScopedTypeVariables #-}
import qualified Data.ByteString.Char8 as BS

main = do
  [r,g,b,n] :: [Int] <- map (read . BS.unpack) . BS.words <$> BS.getLine
  -- n <= 3000
  print (sum [ 1
             | r' <- [0..n `quot` r]
             , g' <- [0..n `quot` g]
             , r * r' + g * g' <= n
             , (n - (r * r' + g * g')) `rem` b == 0
             ] :: Int)