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() - 1;
        long b = sc.nextLong();
        long c = sc.nextLong();
        long d = sc.nextLong();

        long x = lcm(c, d);

        long modB = b - b / c - b / d + b / x;
        long modA = a - a / c - a / d + a / x;

        System.out.println(modB - modA);

    }

    static long lcm (long a, long b) {
        long temp;
        long c = a;
        c *= b;
        while((temp = a%b)!=0) {
            a = b;
            b = temp;
        }
        return c/b;
    }

}
