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) {
		try (Scanner s = new Scanner(System.in)) {
			final long a = s.nextLong();
			final long b = s.nextLong();
			final long c = s.nextLong();
			final long d = s.nextLong();

			if(c == 1 || d == 1) {
				System.out.println("0");
				return;
			}

			long count = 0;

			count += (b / c - (a - 1) / c);
			count += (b / d - (a - 1) / d);
			count -= (b / lcm(c, d) - (a - 1) / lcm(c, d));

			System.out.println(b - a + 1 - count);
		}
	}

	static long lcm(long a, long b) {
		long temp;
		long c = a;
		c *= b;
		while ((temp = a % b) != 0) {
			a = b;
			b = temp;
		}
		return (c / b);
	}

}