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 scanner = new Scanner(System.in)) {
			long a = scanner.nextLong();
			long b = scanner.nextLong();
			long c = scanner.nextLong();
			long d = scanner.nextLong();
			System.out.println(
					b - a - b / c - b / d + b / lcm(c, d) + (a - 1) / c + (a - 1) / d - (a - 1) / lcm(c, d) + 1);
		}
	}

	/**
	 * @param n
	 * @param m
	 * @return nとmの最小公倍数
	 */
	private static long lcm(long n, long m) {
		return n / gcd(n, m) * m;
	}

	/**
	 * @param n
	 * @param m
	 * @return nとmの最大公約数
	 */
	private static long gcd(long n, long m) {
		if (n > m) {
			return gcd(m, n);
		}
		if (0 == n) {
			return m;
		}
		return gcd(n, m % n);
	}
}
