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) {
		Scanner sc = new Scanner(System.in);
		long a = sc.nextLong() - 1;
		long b = sc.nextLong();
		long c = sc.nextLong();
		long d = sc.nextLong();
		long gcd = Euclid(c, d);
		long lcm = c * d / gcd;
		System.out.println(b - b/c - b/d + b/lcm - a + a /c + a/d - a/lcm);
	}
	public static long Euclid(long n, long m) {
		if(m==0) return n;
		return Euclid(m, n%m);
	}
}