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 void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long a = scanner.nextLong();
        long b = scanner.nextLong();
        long c = scanner.nextLong();
        long d = scanner.nextLong();

        long size = b-a + 1;
        long numOfRemoved= 0;
       
        long numOfMultiplyC = b / c - (a -1) / c;
        long numOfMultiplyd = b / d - (a-1) / d;

        long x = c * d / gcd(c, d);
        long numOfMultiplycd = b / x - (a-1) / x;
        
        System.out.println(size - numOfMultiplyC - numOfMultiplyd + numOfMultiplycd);
    }
    

      
    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);
  }
}