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::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

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

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

fn main() {
    input! {
        a: usize,
        b: usize,
        c: usize,
        d: usize,
    }
    let ac = (a - 1) / c;
    let ad = (a - 1) / d;
    let acd = (a - 1) / lcm(c, d);
    let bc = b / c;
    let bd = b / d;
    let bcd = b / lcm(c, d);
    eprintln!("{} {} {}", ac, ad, acd);
    eprintln!("{} {} {}", bc, bd, bcd);
    println!("{}", b + 1 + bcd + ac + ad - a - bc - bd - acd);
}