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 xa = a-1-((a-1)/c+(a-1)/d-(a-1)/lcm(c,d));
      long xb = b-(b/c+b/d-b/lcm(c,d));
      System.out.println(xb-xa);
    }
    public static long lcm(long x,long y){
      return x*y/gcd(x,y);
    }
    public static long gcd(long x,long y){
      if(x < y)return gcd(y,x);
      if(y==0)return x;
      return gcd(y,x%y);
    }
}