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.Arrays;
import java.util.Scanner;

/**
 * Created by Rain on 25/12/13.
 */
public class B275 {
    public static void main(String[] args)
    {
        Scanner in=new Scanner (System.in);
        int n=in.nextInt();
        int k=in.nextInt();
        int a[]=new int [n];
        boolean f[]=new boolean[n];
       // System.out.print(f[0]);
        int j=-1;
        for(int i=0;i<n;i++)
            a[i]=in.nextInt();
        Arrays.sort(a);
        int kq=0;
        for(int i=0;i<n;i++)
        {
            while (j+1<n && (long)a[j+1]*k<=a[i]) j++;
            //System.out.println(j);
            if (j==-1 || f[j]==false || (long)a[j]*k!=a[i]) {
                //System.out.print(a[i]+" ");
                kq+=1; f[i]=true;}
        }
        System.out.println(kq);
    }
}
