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 g = gcd(c,d);
        long q = c * d / g;
        long r = b - a - (((b / c - (a - 1) / c) + b / d - (a - 1) / d) - b / q + (a - 1) / q) + 1;
        System.out.println(r);
    }
    public static long gcd(long a,long b) {
        if(a % b == 0) {
            return b;
        }
        return gcd(b,a % b);
    }
}