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)

solver3::Int->Int->Int->Int->Int
solver3 r g b n = sum [solver2 g b (n-(j*r)) | j<-[0..div n r] ]

solver2::Int->Int->Int->Int
solver2 g b n = sum [solver1 b (n-(j*g)) |j<-[0..div n g]]

solver1::Int->Int->Int
solver1 b n = if mod n b == 0 then 1 else 0

main::IO()
main=do
  (r:g:b:n:[])<-return.map read.words=<<getLine
  print (solver3 r g b n)