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;
using ll = long long;
const ll INF = 1e16;
const ll mod = 1000000007;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

template<class T> inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template<class T> inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
int ctoi(char c) {
  if (c >= '0' && c <= '9') {
    return c - '0';
  }
  return 0;
}
ll factorial(ll n) {
  if (n == 1) {
    return 1;
  }
  ll ans = factorial(n-1);
  return ans*n;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a%b);
}
ll lcm(ll a, ll b) {
  return (a/gcd(a, b))*b;
}
bool is_prime(ll n) {
  for (ll i = 2; i*i <= n; i++) {
    if (n%i == 0) return false;
  }
  return n != 1;
}
ll mod_pow(ll x, ll n, ll mod) {
  if (n == 0) return 1;
  ll res = mod_pow(x*x%mod, n/2, mod);
  if (n & 1) res = res * x % mod;
  return res;
}

int main() {
  ll r, g, b, n;
  cin >> r >> g >> b >> n;
  ll res = 0;
  for (ll i = 0; i*r <= n; i++) {
    for (ll j = 0; j*g <= n-i*r; j++) {
      if ((n-i*r-j*g)%b == 0) res++;
    }
  }
  cout << res << endl;
}