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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)


"use strict";

process.stdin.resume();
process.stdin.setEncoding('utf8');

var g_input = '';
process.stdin.on('data', function(chunk) {
    g_input += chunk;
});

process.stdin.on('end', function() {
    Main(g_input.split(/\r?\n/));
});

function Main(input) {

    const tokens = input[0].split(' ').map(function(value) { return parseInt(value, 10); });
    const r = tokens[0];
    const g = tokens[1];
    const b = tokens[2];
    const n = tokens[3];

    const ans = dfs(0, 0, 0, r, g, b, n);
    console.log(ans);

    return 0;
}

function dfs(rnum, gnum, bnum, r, g, b, n) {
    
    if (n === 0) {
        return 1;
    }

    if (n < 0) {
        return 0;
    }

    let ret = 0;
    if (gnum === 0 && bnum === 0) {
        ret += dfs(rnum + 1, gnum, bnum, r, g, b, n - r)    
    }

    if (bnum === 0) {
        ret += dfs(rnum, gnum + 1, bnum, r, g, b, n - g);
    }

    ret += dfs(rnum, gnum, bnum + 1, r, g, b, n - b);
    
    return ret;
}