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_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()
}

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

fn lcm(a: u64, b: u64) -> u64 {
    a * b / gcd(a, b)
}

fn main(){
    let list: Vec<u64> = read_vec();
    let A = list[0];
    let B = list[1];
    let C = list[2];
    let D = list[3];
    
    let E = lcm(C, D);

    let a = (B / C | 0) - ((A - 1) / C | 0);
    let b = (B / D | 0) - ((A - 1) / D | 0);
    let c = (B / E | 0) - ((A - 1) / E | 0);
    
    println!("{}", (B - A + 1) - (a + b - c));
}