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 sc = new Scanner(System.in);

        final long A = sc.nextLong();
        final long B = sc.nextLong();
        final long C = sc.nextLong();
        final long D = sc.nextLong();
        final long L = lcm(C, D);
        System.out.println((B - B / C - B / D + B / L) - ((A-1) - (A-1) / C - (A-1) / D + (A-1) / L));
    }

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

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