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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    int res = 0;
    int n;
    int[] a;
    int[] work = new int[3];
    void Run()
    {
        var sc = new Scanner();
        a = new int[3];
        for (int i = 0; i < 3; i++) a[i] = sc.NextInt();
        n = sc.NextInt();
        Dfs(0);
        Console.WriteLine(res);
    }

    void Dfs(int c)
    {
        if (c == 2)
        {
            int sum = 0;
            for (int j = 0; j < 2; j++) sum += a[j] * work[j];
            if (n - sum >= 0 && (n - sum) % a[2] == 0) res++;
        }
        else
        {
            for (int i = 0; a[c] * i <= n; i++)
            {
                work[c] = i;
                Dfs(c + 1);
            }
        }
    }

    static void Main(string[] args)
    {
        new Program().Run();
    }

    static long Gcd(long a, long b)
    {
        if (a < b) return Gcd(b, a);
        if (b == 0) return a;
        return Gcd(b, a % b);
    }
}

class Scanner
{
    int index = -1;
    string[] buf;

    public Scanner()
    {
    }

    public int NextInt()
    {
        CheckNext();
        return int.Parse(buf[index++]);
    }

    public long NextLong()
    {
        CheckNext();
        return long.Parse(buf[index++]);
    }

    public double NextDouble()
    {
        CheckNext();
        return double.Parse(buf[index++]);
    }

    public string NextString()
    {
        CheckNext();
        return buf[index++];
    }

    private void CheckNext()
    {
        if (index >= 0 && index < buf.Length) return;

        buf = Console.ReadLine().Split(' ');
        index = 0;
    }
}