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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        r: i64,
        g: i64,
        b: i64,
        n: i64,
    };
    let mut c = 0;
    for x in 0..=3000 {
        let n_r = x * r;
        if n_r > n {
            break;
        }
        for y in 0..=3000 {
            let n_g = y * g;
            if n_r + n_g > n {
                break;
            }
            let z = (n - (n_r + n_g)) / b;
            if !(0..=3000).contains(&z) {
                continue;
            }
            let n_b = z * b;
            if n_r + n_g + n_b == n {
                c += 1;
            }
        }
    }
    let ans = c;
    println!("{}", ans);
}