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 sc = new Scanner(System.in);
		long a =sc.nextLong();
		long b =sc.nextLong();
		long c =sc.nextLong();
		long d=sc.nextLong();
		long ans=0;
		long gcd=gcd(c,d);
		ans+=b-(b/c+b/d-b/(gcd*(c/gcd)*(d/gcd)));
		ans-=a-1-((a-1)/c+(a-1)/d-(a-1)/(gcd*(c/gcd)*(d/gcd)));
		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);
}
}

