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::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let a: i64 = input();
    let b: i64 = input();
    let c: i64 = input();
    let d: i64 = input();

    let g = lcm(c, d);
    let l = b / c - (a - 1) / c;
    let m = b / d - (a - 1) / d;
    let n = b / g - (a - 1) / g;
    println!("{}", b - a + 1 - l - m + n);
}

fn lcm(n: i64, m: i64) -> i64 {
    n * m / gcd(n, m)
}

fn gcd(n: i64, m: i64) -> i64 {
    if m == 0 {
        n
    } else {
        gcd(m, n % m)
    }
}