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::cmp::{max, min};
use std::io::prelude::*;

fn gcd(x: u64, y: u64) -> u64 {
    if x == 0 || y == 0 {
        x + y
    } else {
        gcd(y, x % y)
    }
}

fn main() {
    let mut input_str = String::new();
    std::io::stdin().read_to_string(&mut input_str).unwrap();

    let input_parts = input_str.split_whitespace().collect::<Vec<_>>();
    let mut input_parts_it = input_parts.iter().cloned();

    let a: u64 = input_parts_it.next().unwrap().parse().unwrap();
    let b: u64 = input_parts_it.next().unwrap().parse().unwrap();
    let c: u64 = input_parts_it.next().unwrap().parse().unwrap();
    let d: u64 = input_parts_it.next().unwrap().parse().unwrap();

    let lcm = c * d / gcd(c, d);

    let count = b - a + 1 + ((b / lcm) - ((a + lcm - 1) / lcm) + 1)
        - ((b / c) - ((a + c - 1) / c) + 1)
        - ((b / d) - ((a + d - 1) / d) + 1);

    println!("{}", count);
}