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::*;
use std::cmp::max;

fn main() {
    input! {
        mut a:i64,
        b:i64,
        c:i64,
        d:i64,
    }

    a = a - 1;
    let cd = lcm(c, d);

    let all = b - a;
    let divc = b / c - a / c;
    let divd = b / d - a / d;
    let divcd = b / cd - a / cd;

    println!("{}", all - divc - divd + divcd);
}

fn gcd(x: i64, y: i64) -> i64 {
    if x % y == 0 {
        return y;
    }
    gcd(y, x % y)
}

fn lcm(x: i64, y: i64) -> i64 {
    x / gcd(x, y) * y
}