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 long gcd(long a,long b){
    	if(b==0)
          return a;
      	else
          return gcd(b,a%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 e=c*d/gcd(c,d);
      long sa=(b/c)-((a-1)/c);
      long sb=(b/d)-((a-1)/d);
      long sab=(b/e)-((a-1)/e);
      long diff=b-a+1-sa-sb+sab;
      System.out.print(diff);
      
    }
}