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 OCaml (4.02.3) (judge verdict: Accepted)

let r, g, b, n = Scanf.scanf " %d %d %d %d" @@ fun a b c d -> a, b, c, d
let ans = ref 0
let _ =
  for i = 0 to n do
    for j = 0 to n do
      let rest = n - i * r - j * g in
      if rest >= 0 && rest mod b = 0 then incr ans done done;
  Printf.printf "%d\n" !ans