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<iostream>
#include<algorithm>
#include<climits>
#include<vector>
#include<utility>
#include<cmath>
#include<string>
#include<cstring>
#include<map>
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define prin(arg) std::cout<<arg<<"\n"
#define prin2(arg1,arg2) std::cout<<arg1<<" "<<arg2<<"\n"
#define fill(arg,n) memset(arg,n,sizeof(arg))
using std::cin;
typedef long long ll;
typedef std::pair<int,int> pi;
typedef std::vector<int> vi;
const int INF=1e+9;
const ll INFLL=1e+17;
int R,G,B,N;
void solve(){
  int r=N/R+2,g=N/G+2,cnt=0;
  rep(i,r){
    rep(j,g){
      int x=N-i*R-j*G;
      if(x>=0&&x%B==0) cnt++;
    }
  }
  prin(cnt);
}
int main(){
  cin>>R>>G>>B>>N;
  solve();
  return 0;
}