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: Time Limit Exceeded)


#include "bits/stdc++.h"

// clang-format off
template <typename T> T gcd(T a, T b) { return b == 0 ? a : gcd(b, a % b); }
template <typename T> T lcm(T a, T b) { return a * b / gcd(a, b); }
template <typename T> T clamp(T val, T min, T max) { return val < min ? min : (max < val ? max : val); }
char capitalize(char c) { return static_cast<char>(std::toupper(static_cast<unsigned char>(c))); }
// template <typename T> size_t max_index(T begin, T end) { return distance(begin, max_element(begin, end)); }
// template <typename T> size_t min_index(T begin, T end) { return distance(begin, min_element(begin, end)); }
// clang-format on

#define int long long
#define YES "YES"
#define NO  "NO"
#define MOD 1000000000+7
#define forit(v) for(auto it = v.begin(); it != v.end(); ++it)

using namespace std;

int R;
int G;
int B;
int N;
int RES;



signed main(void) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);

  int num = 0;
  // num = numeric_limits<int>::max();
  // num = numeric_limits<int>::min();
  bool flag = false;
  // flag = true;

  cin >> R >> G >> B >> N;

  for (int r = 0; ; r++) {
    if (r * R == N) ++num;
    if (r * R >= N) break;
    for (int g = 0; ; g++) {
      if (r * R + g * G == N) ++num;
      if (r * R + g * G >= N) break;
      for (int b = 0; ; b++) {
        if (r * R + g * G + b * B == N) ++num;
        if (r * R + g * G + b * B >= N) break;
      }
    }
  }
  
  
  cout << num << endl;
  // cout << (flag ? YES : NO) << endl;
  
  return 0;
}