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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use proconio::{fastout, input};

#[fastout]
fn main() {
    input!(a: usize, b: usize, c: usize, d: usize);

    let ab: u128 = (b - (a - 1)) as u128;

    let cd = yukuriddo(c, d) as u128;

    let abcd = b as u128 / cd - (a - 1) as u128 / cd;

    let ans = (b / c - (a - 1) / c) as u128 + (b / d - (a - 1) / d) as u128 - abcd;

    println!("{}", ab - ans);
}

fn yukuriddo(a_: usize, b_: usize) -> usize {
    let mut a = a_;
    let mut b = b_;
    let x = a * b;
    let tmp;

    /* 自然数 a > b を確認・入替 */
    if a < b {
        tmp = a;
        a = b;
        b = tmp;
    }
    /* ユークリッドの互除法 */
    let mut r = a % b;
    while r != 0 {
        a = b;
        b = r;
        r = a % b;
    }

    return x / b;
}