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 m = lcm(c ,d);

    long x = b - a + 1;
    long y = (b / c) - (a - 1) / c;
    long z = (b / d) - (a - 1) / d;
    long w = (b / m) - (a - 1) / m;
    long ans = x - y - z + w;
    System.out.println(ans);
  }
  
  private static long gcd(long m, long n) {
    if(m < n) return gcd(n, m);
    if(n == 0) return m;
    return gcd(n, m % n);
  }

  private static long lcm(long m, long n) {
      return m * n / gcd(m, n);
  }

}
