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 in = new Scanner(System.in);
        long a = in.nextLong() - 1;
        long b = in.nextLong();
        long c = in.nextLong();
        long d = in.nextLong();

        long s1 = a - (a / c + a / d - a / lcm(c, d));
        long s2 = b - (b / c + b / d - b / lcm(c, d));

        System.out.println(s2 - s1);
    }

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

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