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;

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 lcm = c * d / gcd(c, d);

		long u = b - a + 1;
		long mC = b / c - (a - 1) / c;
		long mD = b / d - (a - 1) / d;
		long mCD = b / lcm - (a - 1) / lcm;

		long ans = u - mC - mD + mCD;

		System.out.println(ans);

		sc.close();
	}

	static long gcd(long m, long n) {
		long tmp;
		while (m % n != 0) {
			tmp = n;
			n = m % n;
			m = tmp;
		}
		return n;
	}
}
