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 p = d, q = c;
        while (p % q != 0) {
            long m = q;
            q = p % q;
            p = m;
        }
        long l = (c * d) / q;
        long counter_b = b - (b / c) - (b / d) + (b / l);
        long counter_a = (a - 1) - ((a - 1) / c) - ((a - 1) / d) + ((a - 1) / l);
        System.out.println(counter_b - counter_a);
        sc.close();
    }
}