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>
#define sz(arr) (int)(arr).size()
#define rng(arr) arr.begin(), arr.end()
#define show(x) cout << #x << " = " << x << endl;

using namespace std;
typedef long long int ll;

void _cin() {}
template <class Head, class... Tail>
void _cin(Head&& head, Tail&&... tail) {
  cin >> head;
  _cin(forward<Tail>(tail)...);
}

#define Cin(T, ...) \
  T __VA_ARGS__;    \
  _cin(__VA_ARGS__)

#define Cins(T, n, xs) \
  vector<T> xs(n);     \
  for (int i = 0; i < n; ++i) cin >> xs[i]

void Main();
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}

void Main() {
  Cin(int, R, G, B, n);

  int ans = 0;
  for (int r = 0; r * R <= n; ++r) {
    for (int g = 0; r * R + g * G <= n; ++g) {
      int b = (n - r * R - g * G) / B;
      if (r * R + g * G + b * B == n && b >= 0) ans++;
    }
  }

  cout << ans << endl;
}