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::{self, BufRead};

fn gcd(x: u64, y: u64) -> u64 {
  let (mut a, mut b) = if x < y {
    (y, x)
  } else {
    (x, y)
  };
  while b != 0 {
    let r = a % b;
    a = b;
    b = r;
  }
  a
}

fn lcm_by_gcd(x: u64, y: u64, g: u64) -> u64 {
  x * y / g
}

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let xs: Vec<u64> = lines.next().unwrap().unwrap().split(' ').map(|x| x.parse().unwrap()).collect();
  let (a, b, c, d) = (xs[0], xs[1], xs[2], xs[3]);
  let g = gcd(c, d);
  let l = lcm_by_gcd(c, d, g);
  let total = b - a + 1;
  let div_c = b / c - (a - 1) / c;
  let div_d = b / d - (a - 1) / d;
  let div_cd = b / l - (a - 1) / l;
  let ans = total - (div_c + div_d - div_cd);
  println!("{}", ans);
}