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.*;

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 cGood = (B / C) - ((A - 1) / C);
        long dGood = (B / D) - ((A - 1) / D);
        long cdGood = (B / lcm(C, D)) - ((A - 1) / lcm(C, D));

        long bad = (B - A + 1) - (cGood + dGood - cdGood);
        System.out.println(bad);
    }

    private static long gcd(long x, long y) {
        return y > 0 ? gcd(y, x % y) : x;
    }

    private static long lcm(long x, long y) {
        return x * (y / gcd(x, y));
    }

}
