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 gcd(x: u64, y: u64) -> u64 {
    let mut x = x;
    let mut y = y;
    while y != 0 {
        let t = y;
        y = x % y;
        x = t;
    }
    x
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let a: u64 = iter.next().unwrap().parse().unwrap();
    let b: u64 = iter.next().unwrap().parse().unwrap();
    let c: u64 = iter.next().unwrap().parse().unwrap();
    let d: u64 = iter.next().unwrap().parse().unwrap();

    let div_c = b/c - (a - 1)/c;
    let div_d = b/d - (a - 1)/d;
    let lcm_cd = c * d / gcd(c, d);
    let div_cd = b/(lcm_cd) - (a - 1)/(lcm_cd);

    let ans: u64 = (b - a + 1) - div_c - div_d + div_cd;

    println!("{}", ans);
}