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();

        // a未満の数で割り切れないｍン
        long c2 = (a - 1) / c;
        long d2 = (a - 1) / d;
        long cd2 = (a - 1) / lcm(c, d);
        long aa = a - (c2 + d2 - cd2);

        //b以下
        long c1 = b / c;
        long d1 = b / d;
        long cd1 = b / lcm(c, d);
        long bb = b - (c1 + d1 - cd1);

        System.out.println(bb - aa + 1);

    }

    private static long gcd(long m, long n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }

    private static long lcm(long m, long n) {
        return m * n / gcd(m, n);
    }

}
