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.io.*;
import java.util.*;
 public class Solution {
	 public static void main(String[] args) throws Exception
    {
		FastReader fr=new FastReader();
		int n=fr.nextInt();
		int k=fr.nextInt();
	long a[]=new long[n];
		for(int i=0;i<n;i++) {
			a[i]=fr.nextInt();
		}
		Arrays.sort(a);
		/*for(int i=0;i<n;i++)
			System.out.print(a[i]+" ");*/
		Set<Long> set=new HashSet<>();
		for(int i=n-1;i>=0;i--) {
			long f=a[i]*k;
			if(!set.contains(f))
				set.add(a[i]);
		}
		//System.out.println(set);
		System.out.println(set.size());
        
        
        
    } 
	 
 }
 class Pair implements Comparable<Pair>{
	 int x,y;
	 Pair(int x,int y){
		 this.x=x;
		 this.y=y;
	 }
	@Override
	public int compareTo(Pair o) {
		return (this.y-o.y);
	}
 }
  

class FastReader
{
    BufferedReader br;
    StringTokenizer st;
 
    public FastReader()
    {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }
 
    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try
            {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt()
    {
        return Integer.parseInt(next());
    }
 
    long nextLong()
    {
        return Long.parseLong(next());
    }
 
    double nextDouble()
    {
        return Double.parseDouble(next());
    }
 
    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}

