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

        final long a = scanner.nextLong();
        final long b = scanner.nextLong();
        final long c = scanner.nextLong();
        final long d = scanner.nextLong();

        final long gcdVal = gcd(c, d);
        final long cd = c * d / gcdVal;

        System.out.println(b - b / c - b / d + b / cd - (a - 1) + (a - 1) / c + (a - 1) / d - (a - 1) / cd);
    }

    private static long gcd(long a, long b) {
        if (a < b) {
            return gcd(b, a);
        }

        if (b == 0) return a;

        return gcd(b, a % b);
    }
}