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.io.*;
public class K_Multiple_Free_Set
{
	public static void main(String args[]) throws Exception
	{
		BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer(f.readLine());
		int runs=Integer.parseInt(st.nextToken());
		int mult=Integer.parseInt(st.nextToken());
		int[] arr=new int[runs];
		st=new StringTokenizer(f.readLine());
		for(int x=0;x<runs;x++)
			arr[x]=Integer.parseInt(st.nextToken());
		Arrays.sort(arr);
		Set<Integer> used=new HashSet<Integer>();
		for(int x=0;x<runs;x++)
			if(arr[x]%mult!=0||!used.contains(arr[x]/mult))
				used.add(arr[x]);
		System.out.println(used.size());
	}
}