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.*;
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();

        if(c<d) {
            long tmp = c;
            c = d;
            d = tmp;
        }

        long cc = c;
        long cd = d;

        long x = c*d;
        long r = c%d;
        while(r!=0) {
            c = d;
            d = r;
            r = c%d;
        }

        x = x/d;


        long l = b/cc + b/cd - b/x;
        long s = (a-1)/cc + (a-1)/cd - (a-1)/x;
        //System.out.println(l +" "+ s);
        System.out.println(b-(a-1)-(l-s));

    }
}