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.*;
import java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long k=sc.nextLong();
		HashSet<Long> hs=new HashSet<Long>();
		long a[]=new long[n];
		for(int i=0;i<n;i++){
		    a[i]=sc.nextLong();
		    hs.add(a[i]);
		}
		Arrays.sort(a);
		//System.out.println(hs.contains(10));
		int ans=0;
		for(int i=0;i<n;i++){
		    if(!hs.contains(a[i])){continue;}
		    ans++;
		    long z=k*a[i];
		    if(hs.contains(z)){hs.remove(z);}
		}
		System.out.println(ans);
	}
}