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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.Arrays;
import java.util.Scanner;

public class Main {

    void run() {
        Scanner sc = new Scanner(System.in);
        int R = sc.nextInt(), G = sc.nextInt(), B = sc.nextInt(), N = sc.nextInt();

        long[] RG = new long[N + 1];
        for (int r = 0; r * R <= N; r++) for (int g = 0; g * G <= N - r * R; g++) {
                RG[r * R + g * G]++;
        }

        long ans = 0;
        for (int rg = 0; rg <= N; rg++) for (int b = 0; b * B <= N - rg; b++) {
            if (N == rg + b * B)
                ans += RG[rg];
        }
//        debug(RG);
        System.out.println(ans);
    }

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}