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;

public class Main {

    private static long lcm(long a, long b) {
        long temp;
        long c = a * b;
        while ((temp = a % b) != 0) {
            a = b;
            b = temp;
        }
        return c / b;
    }

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