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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main()
{
  int r, g, b, n;
  cin >> r >> g >> b >> n;
  int ans = 0;
  for(int x = 0; x <= n; ++x)
  {
    int tmp_r = r * x;
    for(int y = 0; y <= n; ++y)
    {
      int tmp_g = g * y;
      for(int z = 0; z <= n; ++z)
      {
        int tmp_b = b * z;
        if(tmp_r + tmp_g + tmp_b == n) ++ans;
        else if(tmp_b > n || tmp_g + tmp_b > n || tmp_r + tmp_g + tmp_b > n) break;
      }
      if(tmp_g > n || tmp_r + tmp_g > n) break;
    }
    if(tmp_r > n) break;
  }
  cout << ans << endl;
}