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::vec::Vec;
use std::cmp::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
  let (a, b, c, d) = {
    let v: Vec<u64> = read_vec();
    (v[0], v[1], v[2], v[3])
  };

  let n_c: u64 = b / c - (a - 1) / c;
  let n_d: u64 = b / d - (a - 1) / d;
  let lcm = (c * d) / gcd(c, d);
  let n_cd: u64 = b / lcm - (a - 1) / lcm;

  println!("{}", (b - a + 1) - (n_c + n_d - n_cd));
}


fn gcd(a: u64, b: u64) -> u64 {


  if b > a {
    gcd(b, a);
  }

  if a % b == 0 {
    return b;
  }

  let r: u64 = a % b;

  return gcd(b, r);
}