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 (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::Read;
use std::io::{stdout, BufWriter, Write};
use std::cmp::min;
use std::cmp::max;

fn main() {
    let mut buf = String::new();

    // stdinから全てbufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();

    // 読み込んだ文字列をスペースで分解する
    let mut iter = buf.split_whitespace();

    // about r
    let r: usize = iter.next().unwrap().parse().unwrap();
    // about g
    let g: usize = iter.next().unwrap().parse().unwrap();
    // about b
    let b: usize = iter.next().unwrap().parse().unwrap();
    // about n
    let n: usize = iter.next().unwrap().parse().unwrap();

    // ans
    let mut ans: usize = 0;

    let weight_min: usize = min(r, min(g, b));
    let loop_min: usize = (n + 1) / weight_min + 1;

    let weight_max: usize = max(r, min(g, b));
    let loop_max: usize = (n + 1) / weight_max + 1;

    let weight_mid: usize = r + g + b - weight_min - weight_max;
    let loop_mid: usize = (n + 1) / weight_mid + 1;
    
    for i_min in 0..loop_min {
        for i_mid in 0..loop_mid {
            for i_max in 0..loop_max {
                let num_ball: usize = i_min * weight_min + i_mid * weight_mid + i_max * weight_max;
                if num_ball == n {
                    ans += 1;
                }
            }
        }
    }

    // 出力
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
    writeln!(out, "{}", ans).unwrap();
}