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)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        a: u128,
        b: u128,
        c: u128,
        d: u128
    };

    let start_to_a_with_c = (a - 1) / c;
    let start_to_b_with_c = b / c;

    let start_to_a_with_d = (a - 1) / d;
    let start_to_b_with_d = b / d;

    let x = start_to_b_with_c - start_to_a_with_c + start_to_b_with_d - start_to_a_with_d;

    let lcm_cd = lcm(c, d);

    let start_to_a_with_cd = (a - 1) / lcm_cd;
    let start_to_b_with_cd = b / lcm_cd;

    let y = start_to_b_with_cd - start_to_a_with_cd;

    println!("{}", (b - a + 1) - (x - y));
}

fn lcm(a: u128, b: u128) -> u128 {
    let mut a = a;
    let mut b = b;

    let x = a * b;

    if a > b {
        let tmp = a;
        a = b;
        b = tmp;
    }

    let mut r = a % b;

    while r != 0 {
        a = b;
        b = r;
        r = a % b;
    }

    return x / b;
}