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();
	long cd = lcm(c,d);
	System.out.print(b-a+1-(b/c - (a-1)/c + b/d - (a-1)/d - b/cd + (a-1)/cd));
    }
    static long gcd(long m, long n) {
	if (m < n) {
	    long tmp = m;
	    m = n;
	    n = tmp;
	}
	long rem = 0;
	while ((rem = m%n) != 0) {
	    m = n;
	    n = rem;
	}
	return n;
    }
    static long lcm(long m, long n) {
	return m * n / gcd(m, n);
    }
}
