Problem:
Score : 300 points

Problem Statement

You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

1\leq A\leq B\leq 10^{18}

1\leq C,D\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let abcd = read_vec::<u64>();
    let a = abcd[0];
    let b = abcd[1];
    let c = abcd[2];
    let d = abcd[3];

    let n = b - a + 1;
    let lcm = c * d / gcd(c, d);
    let d = {
        let c_div = b / c - (a - 1) / c;
        let d_div = b / d - (a - 1) / d;
        let cd_div = b / lcm - (a - 1) / lcm;
        c_div + d_div - cd_div
    };

    println!("{}", n - d);
}

fn gcd(a: u64, b: u64) -> u64 {
    if a % b == 0 {
        b
    } else {
        gcd(b, a % b)
    }
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}