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 read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let a: usize = scan(tokens);
    let b: usize = scan(tokens);
    let c: usize = scan(tokens);
    let d: usize = scan(tokens);
    let l = lcm(c, d);
    println!(
        "{}",
        ((b - b / c) - (b / d - b / l)) - (((a - 1) - (a - 1) / c) - ((a - 1) / d - (a - 1) / l))
    );
}

fn lcm(x: usize, y: usize) -> usize {
    x / gcd(x, y) * y
}

fn gcd(mut x: usize, mut y: usize) -> usize {
    while y != 0 {
        let r = x % y;
        x = y;
        y = r;
    }
    x
}