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;

macro_rules! get {
    ($t: ty) => {
        {
            let mut x = String::new();
            io::stdin().read_line(&mut x).ok();
            x = x.trim_right().to_owned();
            x.parse::<$t>().unwrap()
        }
    };
    ($($t: ty), *) => {
        {
            let mut x = String::new();
            io::stdin().read_line(&mut x).ok();
            x = x.trim_right().to_owned();
            let mut inter = x.split_whitespace();
            (
                $(inter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
}

macro_rules! insert_vec {
    ($t: ty) => {
        {
            let mut x = String::new();
            io::stdin().read_line(&mut x).ok();
            x = x.trim_right().to_owned();
            x.split_whitespace().map(|x| x.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
}

macro_rules! word_chars_vec {
    () => {
        {
            let mut x = String::new();
            io::stdin().read_line(&mut x).ok();
            x = x.trim_right().to_owned();
            x.chars().collect::<Vec<_>>()
        }        
    };
}


fn gcd (i: i64, j: i64) -> i64 {
    if i == 0 {
        j 
    }
    else {
        gcd(j % i, i)
    }
}

fn lcm (i: i64, j: i64) -> i64 {
    i / gcd(i, j) * j
}


fn main() {
    let (a, b, c, d) = get!(i64, i64, i64, i64);
    let b_c_count = b / c;
    let b_d_count = b / d;
    let b_dup_count = b / lcm(c, d);
    let b_count = b_c_count + b_d_count - b_dup_count;

    let a_c_count = (a - 1) / c;
    let a_d_count = (a - 1) / d;
    let a_dup_count = (a - 1) / lcm(c, d);
    let a_count = a_c_count + a_d_count - a_dup_count;

    println!("{}", b - a - (b_count - a_count) + 1);

}