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() {
  vector<int> col(3);
  int n;
  cin >> col.at(0) >> col.at(1) >> col.at(2) >> n;
  int rmax, gmax, bmax;
  sort(col.begin(), col.end());
  rmax=n/col.at(0); gmax=n/col.at(1); bmax=n/col.at(2);
  int count=0;
  for (int i=0; i<rmax+1; i++) {
    for (int j=0; j<gmax+1; j++) {
      for (int k=0; k<bmax+1; k++) {
        if (col.at(0)*i+col.at(1)*j+col.at(2)*k==n) {
          count++;
        }
        if (col.at(0)*i+col.at(1)*j+col.at(2)*k>n) {
          break;
        }
      }
      if (col.at(0)*i+col.at(1)*j>n) {
          break;
      }
    }
/*    if (r*i>n) {
          break;
    }*/
  }
  cout << count <<endl;
}