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 (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
use std::io::*;
use std::str::FromStr;

use std::cmp::{max, min};

fn main() {
    input! {
        a: i64,
        b: i64,
        c: i64,
        d: i64,
    }
    println!("{}", (b - a + 1) - (lambda(b, c, d) - lambda(a - 1, c, d)));
}

fn lambda(i: i64, c: i64, d: i64) -> i64 {
    // println!("gcd:{}", gcd(c, d));
    return (i / c) + (i / d) - (i / (lcm(c, d)));
}

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

fn lcm(x: i64, y: i64) -> i64 {
    x * (y / gcd(x, y))
}