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.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long a=sc.nextLong(),b=sc.nextLong(),c=sc.nextLong(),d=sc.nextLong();
        long ans=0;
        ans+=b/c-(a-1)/c;
        ans+=b/d-(a-1)/d;
        ans-=b/(c*d/Euclid(c,d))-(a-1)/(c*d/Euclid(c,d));
        System.out.println(b-a+1-ans);

    }
    private static long Euclid(long n, long m) {
        long tmp;
        while (true) {
            if (n == 0) {
                return m;
            } else if (m == 0) {
                return n;
            }
            tmp = n;
            n = m;
            m = tmp;
            n = n % m;

        }

    }

}
