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()-1;
		long b = sc.nextLong();
		long c = sc.nextLong();
		long d = sc.nextLong();
		
		long l = lcm(c,d);

		long countA = a - (a/c + a/d - a/l);
		long countB = b - (b/c + b/d - b/l);
		
		long ans = countB - countA;
		System.out.println(ans);
		
		
		sc.close();
	}
	
	public static long lcm(long a, long b)  {
		long c = a * b;
		long temp;
		while ((temp = a % b) != 0) {
			a = b;
			b = temp;
		}
		
		return c/b;
	}
	
}
