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 ans = b / c - (a - 1) / c + b / d - (a - 1) / d - (b / lcm(c, d) - (a - 1) / lcm(c, d));
        System.out.println(b - a + 1 - ans);
    }

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

    static long gcd(long x, long y) {
        if (x < y)
            return gcd(y, x);
        if (y == 0)
            return x;
        return gcd(y, x % y);
    }
}
