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.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
import java.util.Scanner;

/**
 * test
 */
public class Main {

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

        long lcm = c * d / gcd(c, d);
        //System.out.println(lcm);

        System.out
                .println(b - a + 1 - (b / c) - (b / d) + ((a - 1) / c) + ((a - 1) / d) + ((b / lcm) - ((a - 1) / lcm)));
    }

    private static long gcd(long a, long b) {
        while (b > 0) {
            long tmp = a % b;
            a = b;
            b = tmp;
        }
        return a;
    }
}