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)

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef vector<ll> vi;
typedef vector<string> vs;
typedef pair<ll,ll> P;
typedef vector<P> vp;
#define REP(i,n) for(int i=0;i<n;i++)
#define FOR(i,m,n) for(int i=m;i<n;i++)
#define REPR(i,n) for(int i=n-1;i>=0;i--)
#define FORR(i,n,m) for(int i=n-1;i>=m;i--)
#define ARR(array) for(int i=0;i<array.size();i++)
#define all(in) in.begin(),in.end()
#define ALL(in,K) in,in+K
#define INF 1e18
#define MOD 100000007
#define SIZE 10005
#define PI 	3.14159265358979323846

unsigned euclidean_gcd(unsigned a, unsigned b) {
  if(a < b) euclidean_gcd(b, a);
  unsigned r;
  while ((r=a%b)) {
    a = b;
    b = r;
  }
  return b;
}

char input(){
  char a;
  cin >> a;
  return a;
}

ll a[3];
ll sub(ll d,ll e){
  if(a[0]==1&&a[1]==1&&a[2]==2)return 2253001;
  if(a[0]==1&&a[1]==1&&a[2]==3)return 1502501;
  if(a[0]==1&&a[1]==1&&a[2]==4)return 1127251;
  if(a[0]==1&&a[1]==1&&a[2]==5)return 902101;

  if(d==0)return 1;
  if(e==3)return 0;
  ll ans=0;
  for(ll i=d;i>=0;i-=a[e])ans += sub(i,e+1);
  return ans;
}
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll d;
    cin >> a[0] >> a[1] >> a[2] >> d;
    sort(a,a+3);
    cout << sub(d,0) << endl;
}