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::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let a: u64 = iterator.next().unwrap().parse().unwrap();
    let b: u64 = iterator.next().unwrap().parse().unwrap();
    let c: u64 = iterator.next().unwrap().parse().unwrap();
    let d: u64 = iterator.next().unwrap().parse().unwrap();

    let gcd = if c > d { gcd(c, d) } else { gcd(d, c) };
    let k = c / gcd * d;

    let x = b / c + b / d - b / k;
    let y = (a - 1) / c + (a - 1) / d - (a - 1) / k;

    let ans = (b - x) - (a - 1 - y);

    return ans.to_string();
}

fn gcd(m: u64, n: u64) -> u64 {
    assert_eq!(m >= n, true);

    if n == 0 {
        m
    } else {
        gcd(n, m % n)
    }
}