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>
typedef long long ll;
typedef long double ld;
using namespace std;

#define REP(i, l, n) for(int i=(l), i##_len=(n); i<i##_len; ++i)
#define ALL(x) (x).begin(),(x).end()
#define pb push_back

ll gcd(ll a,ll b){return b ? gcd(b,a%b) : a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

int dx[4] = {-1, 1, 0, 0};
int dy[4] = {0, 0, 1, -1};

int main(){
    int R, G, B, n; cin >> R >> G >> B >> n;
    int ans = 0;
    REP(i, 0, n/R+1){
        REP(l, 0, n/G+1){
            int k = i * R + l * G;
            if(n-k >= 0 && (n-k)%B == 0){
                ans++;
            }
        }
    }
    cout << ans << endl;
}