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 static java.util.Arrays.* ;
import static java.lang.Math.*  ;
import java.io.*;
import java.util.*;


public class Main
{
    void main() throws Exception
    {
        Scanner sc = new Scanner(System.in) ;
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt() , k = sc.nextInt() ;
        Integer [] a = new Integer [n] ;
        TreeSet<Long> set = new TreeSet<>() ;
        for(int i = 0 ; i < n ;i ++)
            a[i] = sc.nextInt() ;
        sort(a);
        int [] cnt = new int [2] ;
        for(int i = 0 ; i < n ;i ++)
            if(set.contains(1L * a[i]))
                cnt[1]++ ;
            else
            {
                set.add(1L * a[i] * k) ;
                cnt[0] ++ ;
            }
        out.println(max(cnt[0] , cnt[1]));
        out.flush();
    }
    public static void main(String[] args) throws Exception { new Main().main(); }

    class Scanner
    {
        BufferedReader br ;
        StringTokenizer st ;

        Scanner(InputStream in)
        {
            br = new BufferedReader(new InputStreamReader(in)) ;
        }
        String next() throws Exception
        {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken() ;
        }
        int nextInt() throws Exception { return Integer.parseInt(next()) ; }

        long nextLong() throws Exception {return Long.parseLong(next());}

        double nextDouble() throws Exception {return Double.parseDouble(next());}

    }
}