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);
        long a = sc.nextLong();
        long b = sc.nextLong();
        long c = sc.nextLong();
        long d = sc.nextLong();

        long start = f(a-1,c,d);
        long end = f(b,c,d);

        System.out.print(end -start);
    }

    public static long f(long a, long b, long c) {
        long result = a;
        result -= a / b;
        result -= a / c;
        result += a / lcm(b, c);
        return result;
    }

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

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