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[]) throws Exception {
        Scanner sc = new Scanner(System.in);
        long a = sc.nextLong();
        long b = sc.nextLong();
        long c = sc.nextLong();
        long d = sc.nextLong();
        
        long cntA = 0;
        long cntB = 0;
        long lcm = lcm(c, d);

  
        cntA = a - a / c - a / d + a / lcm(c, d);
        cntB = b - b / c - b / d + b / lcm(c, d);
 
        long res = (cntB - cntA);
        if(a % c != 0 && a % d != 0) res++;
        System.out.println(res);
    }

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

    private static long lcm(long a, long b) {
    	return a / gcd(a, b) * b;
    }

}


