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 lcm = (C * D) / gcd(D, C);
    
    System.out.println(count(B, C, D, lcm) - count(A-1, C, D, lcm));
  }
  
  private static long gcd(long a, long b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a%b);
  }
  
  private static long count(long n, long C, long D, long lcm) {
    return n - n/C - n/D + n/lcm;
  }
}