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.Scanner;
public class Main{
  public static long gcd(long a, long b){
    if(a < b) {
      long tmp = a;
      a = b;
      b = tmp;
    }
    if(b==0) return a;
    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();
    a -= 1;
    
    long lcm = c * d / gcd(c,d);
    long n = b - (b/c) - (b/d) + (b/lcm);
    long m = a - (a/c) - (a/d) + (a/lcm);
    
    System.out.println(n-m);
  }
}
