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_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn count(a: i64, b: i64, m: i64) -> i64 {
    if a == b {
        if a % m == 0 {
            return 1;
        } else {
            return 0;
        }
    }
    let end_a = ((a - 1) / m) * m + 1;
    let start_b = (b / m) * m;
    if end_a > start_b {
        debug!(a, b, m);
        return 0;
    }
    let ret = (start_b - end_a) / m + 1;
    debug!(a, b, m, ret);
    ret
}

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        return a;
    }
    gcd(b, a % b)
}

fn main() {
    let v = read_vec::<i64>();
    let (a, b, c, d) = (v[0], v[1], v[2], v[3]);
    let ans = b - a + 1 - count(a, b, c) - count(a, b, d) + count(a, b, c * d / gcd(c, d));
    println!("{:?}", ans);
}

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(|e| e.parse().ok().unwrap())
        .collect()
}