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.*;
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();
		System.out.println(b-a+1 - div(a,b,c) - div(a,b,d) + div(a,b,c*d/gcd(c,d)));
	}
	static long div(long x, long y, long z){
		return y / z - (x-1) / z;
	}
	static long gcd(long a, long b){
		if(a < b) return gcd(b, a);
		if(b == 0) return a;
		else return gcd(b, a % b);
	}
}
