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)

#ifdef __GNUC__ 
#include <bits/stdc++.h>
auto & in = std::cin;
#else
std::istringstream in;
#endif
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/dynamic_bitset.hpp>
using namespace std;
#define ALL(v) std::begin(v),std::end(v)
using u6 = std::uint64_t;

struct Calc {
};
int main() {
#ifndef __GNUC__ 
	in.str("1 2 3 4");
#endif
	int R, G, B, N;
	array<int,3> RGB;
	u6 count = 0;
	for (auto &rgb : RGB)in >> rgb;
	in >> N;
	sort(ALL(RGB),std::greater<>());
	for (int r = 0; r<=N; r += RGB[0]) {
		for (int g = 0; r+g<=N; g += RGB[1]) {
			if ((N-r-g)%RGB[2]==0)++count;
		}
	}
	cout << count << endl;
}