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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <climits>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <bitset>
#include <utility>
#include <numeric>
#include <queue>
#include <stack>

using ll = long long;
using namespace std;

constexpr int MOD = 1e9 + 7;
constexpr ll MOD_LL = ll(1e9 + 7);

int main(void) {
	ll R, G, B, N;
	cin >> R >> G >> B >> N;
	
	ll ans = 0LL;
	for(ll r = 0; r <= N; ++ r) {
		for(ll g = 0; g <= N; ++g) {
			ll b = (N - R * r - G * g) / B;
			
			if( b >= 0 && R * r + G * g + B * b == N ) {
				ans++;
			}
		}
	}
	
	cout << ans << endl;
	
	return 0;
}