A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.
import java.util.*;

public class Main
{
    public static void main(String[] arg)
    {
        Scanner scan=new Scanner (System.in);
        int n = scan.nextInt();
        int k=scan.nextInt();
        int [] numbers = new int [n];
        for (int i=0;i<n;i++)
            numbers[i]=scan.nextInt();
        Arrays.sort(numbers);
        Set<Integer> num = new TreeSet<Integer>();
        for (int i=0;i<n;i++)
        {
            if (numbers[i]%k==0)
            {
                if (!num.contains(numbers[i]/k))
                    num.add(numbers[i]);
            }
            else
                num.add(numbers[i]);

        }
        System.out.println(num.size());
    }

}
