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)

import Control.Applicative
import Control.Monad

main :: IO ()
main = do
    [r, g, b, n] <- map read . words <$> getLine
    print $ length [() |
        nr <- [0..(div n r)],
        ng <- [0..(div (n-nr*r) g)],
        nb <- [0..(div (n-nr*r-ng*g) b)],
        nr*r + ng*g + nb*b == n]