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)

#[allow(unused_macros)]
macro_rules! invec {
    ( $t:ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s.trim().split_whitespace().map(|s| s.parse::<$t>().unwrap()).collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }}
}

#[allow(unused_macros)]
macro_rules! input {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($(
            {
                 splits.next().unwrap().parse::<$t>().unwrap()
            },
        )*)
    }}
}

fn count(n: u64, c: u64, d: u64) -> u64 {
    n - ((n / c) + (n / d) - (n / (c * d / gcd(c, d))))
}

fn gcd(n: u64, m: u64) -> u64 {
    match (n, m) {
        (n, 0) => return n,
        (0, m) => return m,
        (n, m) => {
            let r = n % m;
            if r == 0 {
                m
            } else {
                gcd(m, r)
            }
        },
    }
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (a, b, c, d) = input!(u64, u64, u64, u64);

    println!("{}", count(b, c, d) - count(a - 1, c, d));
}

fn main() {
    solve();
}