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<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn gcd(a: usize, b: usize) -> usize {
    if a % b == 0 {
        b
    } else {
        gcd(b, a % b)
    }
}
fn lcm(a: usize, b:usize) -> usize {
    a / gcd(a, b) * b
}



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

    let mut count = b - a + 1;

    let c_div = b / c - (a-1) / c;
    let d_div = b / d - (a-1) / d;
    let lcm = lcm(c, d);
    let lcm_div = b / lcm - (a-1) / lcm;

    count -= c_div;
    count -= d_div;
    count += lcm_div;

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