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) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
		String str = scan.nextLine();

		long a = Long.parseLong(str.split(" ")[0]);
		long b = Long.parseLong(str.split(" ")[1]);
		long c = Long.parseLong(str.split(" ")[2]);
		long d = Long.parseLong(str.split(" ")[3]);

		 a -= 1;

		long an = (a - a/c - a/d + (a/(lcm(c, d))));
		long bn = (b - b/c - b/d + (b/(lcm(c, d))));

		System.out.println(bn - an);


	}

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