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);
		// 整数の入力
		long A = sc.nextLong();
      long B = sc.nextLong();
      long C = sc.nextLong();
      long D = sc.nextLong();
      long bmade = B/C+B/D-B/(lcm(C,D));
      long amade = (A-1)/C+(A-1)/D-(A-1)/(lcm(C,D));
      

 
      System.out.println(B-A-(bmade-amade)+1);
    }
  
  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);
}
}