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: Accepted)

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

int main(){
    int r,g,b,a[3],n;
    int ans=0;
    cin >>a[0]>>a[1]>>a[2]>>n;
    vector<int> vx(a,a+3);
    sort(vx.begin(),vx.end());

    for (int i = 0; i <= n/vx[2]; i++){
        for (int j = 0; j <= n/vx[1]; j++){
            if((n-(i*vx[2]+j*vx[1])) % vx[0] == 0 && (n>=(i*vx[2]+j*vx[1])) )ans++;
        }
    }
    
    cout << ans <<endl;
    return 0;
}