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: Time Limit Exceeded)

use whiteread::parse_line;

/*
fn calc(n: usize, r: usize, g: usize, b: usize, dp: &mut Vec<usize>) -> usize {
    if dp[n] == std::usize::MAX {
        let mut res = 0;
        if n >= r {
            res += dp[n - r];
        }
    }
    dp[n]
}
*/

fn main() {
    let (r, g, b, n): (usize, usize, usize, usize) = parse_line().unwrap();
    let mut cnt = 0;
    //let mut dp: Vec<usize> = vec![std::usize::MAX; n + 1];

    //println!("{}", calc(n, r, g, b, &mut dp));
    for x in 0..=3000 {
        if x > n {
            break;
        }
        for y in 0..=3000 {
            if x * r + y * b > n {
                break;
            }
            for z in 0..=3000 {
                if x * r + y * b + z * g > n {
                    break;
                }
                if x * r + y * b + z * g == n {
                    cnt += 1;
                }
            }
        }
    }
    println!("{}", cnt);
}