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 delme {


    public static void main(String args[] ) throws IOException 
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pout = new PrintWriter(new BufferedOutputStream(System.out));

        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());

        HashSet<Long> map = new HashSet<>();
        long[] arr = new long[n];
        int res = 0;
        st = new StringTokenizer(br.readLine());

        for(int i = 0;i < n;i++)
        {
            arr[i] = Long.parseLong(st.nextToken());
            
        }
        Arrays.sort(arr);
        for(int i = 0;i < arr.length;i++)
        {
            if(!map.contains(arr[i]))
            {
                res++;
                map.add(k*arr[i]);
            }
        }

        pout.println(res);   
        pout.flush();

    }
}
