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();
		long B = sc.nextLong();
		long C = sc.nextLong();
		long D = sc.nextLong();
		sc.close();
		long lcm =C*D/gcd(C,D);
		long sumA = (A-1) - (A-1)/C -(A-1)/D + (A-1)/lcm;
		long sumB = B - B/C -B/D + B/lcm;
		System.out.println(sumB - sumA);
	}

	private static long gcd(long a,long b) {
		if(a < b) {
			return gcd(b, a);
		}
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
}