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 (1.15.1) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        return a;
    }
    gcd(b, a % b)
}

#[allow(dead_code)]
fn lcm(a: i64, b: i64) -> i64 {
    a / gcd(a, b) * b
}

fn calc(a: i64, b: i64) -> i64 {
    a / b
}

fn main() {
    let a = read::<i64>();
    let b = read::<i64>();
    let c = read::<i64>();
    let d = read::<i64>();
    let e = lcm(c, d);
    let mut ans = b - a + 1;
    ans -= calc(b, c);
    ans += calc(a - 1, c);
    ans -= calc(b, d);
    ans += calc(a - 1, d);
    ans += calc(b, e);
    ans -= calc(a - 1, e);
    println!("{}", ans);
}