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 {

	// c < d
	public static long eukleides(long c, long d){
		if(d % c == 0){
			return c;
		}

		long mod = d % c;

		return eukleides(mod, c);
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);

		// input
		long a = scan.nextLong();
		long b = scan.nextLong();
		long c = scan.nextInt();
		long d = scan.nextInt();
		if(c > d){
			long temp = c;
			c = d;
			d = temp;
		}

		long gcd = eukleides(c, d);
		long lcm = (c * d) / gcd;
		long answer = b - b / c - b / d + b / lcm;
		answer -= a - 1 - (a - 1) / c - (a - 1) / d + (a - 1) / lcm;

		System.out.println(answer);

	}
}

