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 long gcd(long a, long b) {
        while (a % b != 0) {
            long tmp = a % b;
            a = b;
            b = tmp;
        }
        return b;
    }
    public static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }
    public static long divnum(long a, long b, long x) {
        return b / x - (a - 1) / x;
    }
    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();

        if (d % c == 0) {
            System.out.println(b - a + 1- divnum(a, b, c));
        } else {
            System.out.println(b - a + 1- divnum(a, b, c) - divnum(a, b, d) + divnum(a, b, lcm(c, d)));
        }
    }
}
