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 e = lcm(c,d);
    long count = b-a+1;
    count -= b/c - (a-1)/c;
    count -= b/d - (a-1)/d;
    count += b/e - (a-1)/e;
    System.out.println(count);

  }

  private static long lcm(long a, long b){
    long temp;
    long c = a;
    c *= b;
    while((temp = a%b)!=0){
      a=b;
      b=temp;
    }
    return c/b;
  }
}
