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();
     long b = sc.nextLong();
     long  c = sc.nextLong();
     long d = sc.nextLong();
     long cd,x,y,z,ans;
     cd = lcm(c,d);
     x= b/c -(a-1)/c;
     y= b/d -(a-1)/d;
     z= b/cd -(a-1)/cd;
     ans= b-a+1-x-y+z;
     System.out.println(ans);
   }

   private static long gcd(long m, long n) {
       if(m < n) return gcd(n, m);
       if(n == 0) return m;
       return gcd(n, m % n);
   }

   private static long lcm(long m, long n) {
       return m * n / gcd(m, n);
   }
}
