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.sscanf (read_line ()) "%d %d %d %d" @@ fun r g b n -> (r, g, b, n)

let () =
  let ans = ref 0 in
  for i = 0 to n / r do
    for j = 0 to n / g do
      let sum = r * i + j * g in
      if sum <= n && (n - sum) mod b = 0 then ans := !ans + 1
    done
  done;
  Printf.printf "%d\n" !ans