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)

use std::io;


fn main() {
    let (a, b, c, d) = {
        let i = read::<usize>();
        (i[0], i[1], i[2], i[3])
    };
    println!("{}", b - a - (calc(b, c, d) - calc(a - 1, c, d)) + 1);
}

fn calc(n: usize, a: usize, b: usize) -> usize {
    let da: usize = n / a;
    let db: usize = n / b;
    da + db - n / lcm(a, b)
}

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

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


#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
std::str::FromStr,
T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
std::str::FromStr,
T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}