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.*;

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 count = B/C - A/C;
        if (A % C == 0) {
            count++;
        }
        count += B/D - A/D;
        long lcm = lcm(C, D);
        count -= (B / lcm) - (A / lcm);

        System.out.println(B - A + 1 - count);
    }

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

    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);
    }
}

