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::{input, fastout};
use proconio::marker::*;

#[fastout]
fn main() {
    input! {
    a: usize,
    b: usize,
    c: usize,
    d: usize
    }
    let cd = c * d / gcd(&c, &d);
    let ans = (b - a + 1) + count(cd, a, b) - count(c, a, b) - count(d, a, b);
    println!("{}", ans);
}

fn count(t: usize, a: usize, b: usize) -> usize {
    b / t - if a % t == 0 {a / t - 1} else {a / t}
}

// O(log(N))
fn gcd(a: &usize, b: &usize) -> usize {
    let (mut x, mut y) = if a < b { (*b, *a) } else { (*a, *b) };
    let mut r = x % y;
    while r != 0 {
        x = y;
        y = r;
        r = x % y;
    }
    y
}