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 {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        long a = scanner.nextLong() - 1;
        long b = scanner.nextLong();
        long c = scanner.nextLong();
        long d = scanner.nextLong();
        long e = lcm(c, d);
        System.out.println((b - a) - (b / c - a / c) - (b / d - a / d) + (b / e - a / e));
    }

    static long gcd(long a, long b) {
        return 0 < b ? gcd(b, a % b) : a;
    }

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