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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long a = Long.parseLong(sc.next());
        long b = Long.parseLong(sc.next());
        long c = Long.parseLong(sc.next());
        long d = Long.parseLong(sc.next());

        long n = b - a + 1;
        long cc = (b / c) - ((a - 1) / c);
        long dd = (b / d) - ((a - 1) / d);
        long cd = (b / lcm(c, d)) - ((a - 1) / lcm(c, d));

        System.out.println(n - cc - dd + cd);

    }

    static long gcd(long a, long b) {
        return b > 0 ? gcd(b, a % b) : a;
    }

    static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }
}