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 = Long.parseLong(sc.next()) -1;
        long b = Long.parseLong(sc.next());
        int c = Integer.parseInt(sc.next());
        int d = Integer.parseInt(sc.next());
        
        long a2 = a -(a/c) -(a/d) +(a / lcm(c, d));
        long b2 = b -(b/c) -(b/d) +(b / lcm(c, d));
        System.out.println(b2-a2);
    }
    
    private static long gcd(long a, long b){
        
        if(b == 0){
            return a;
        }else{
            return gcd(b, a % b);
        }
    }
    
    private static long lcm(long a, long b){
        
        return (a / gcd(a, b)) * b;
    }
}