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: Time Limit Exceeded)

main :: IO ()
main = do
  [r, g, b, n] <- map read . words <$> getLine
  print $ solve' r g b n

solve :: Int -> Int -> Int -> Int -> Int
solve r g b n =
  length $ filter ((n ==) . sum) $ sequence [rs, gs, bs]
  where
    rs = [0, r .. n]
    gs = [0, g .. n]
    bs = [0, b .. n]

solve' :: Int -> Int -> Int -> Int -> Int
solve' r g b n =
  length $ filter ((n ==) . sum) rgbs
  where
    rgbs =
      [ [r', g', b']
      | r' <- [0, r .. n]
      , g' <- [0, g .. (n - r')]
      , b' <- [0, b .. (n - r' - g')]
      ]