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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long A = sc.nextLong() -1;
    long B = sc.nextLong();
    long C = sc.nextLong();
    long D = sc.nextLong();
    long E = lcm(C,D);
    
    long big = B - B/C - B/D + B/E;
    long small = A -A/C -A/D + A/E;
    System.out.println(big-small);
    
  }
  private static long lcm(long m,long n){
    return m*n/gcd(m,n);
  }
  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);
  }
}