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 lcm(a: usize, b: usize) -> usize {
    let mut x = std::cmp::max(a, b);
    let mut y = std::cmp::min(a, b);
    while y != 0 {
        let tmp = y;
        y = x % y;
        x = tmp;
    }
    a * b / x
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    let v: Vec<usize> = buf.split_whitespace().map(|x| x.parse().unwrap()).collect();
    let (a, b, c, d) = (v[0], v[1], v[2], v[3]);
    let a = a - 1;
    let lcm = lcm(c, d);
    let mut ans = b - a;
    ans -= b / c - a / c;
    ans -= b / d - a / d;
    ans += b / lcm - a / lcm;
    println!("{}", ans);
}