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 kMultipleFree274A
{

    public static class MyFasterScanner 
    {
        BufferedReader br;
        StringTokenizer st;

        public MyFasterScanner() {
            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().toString();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    public static void main(String[] args) 
    {
        // Set up scanner
        MyFasterScanner sc = new MyFasterScanner(); 
        // System.out.println("Input n");
        int n = sc.nextInt();
        // System.out.println("Input k");
        long k = sc.nextInt();
        
        ArrayList<Long> a = new ArrayList<Long>();
        for (int i=0; i<n; i++)
        {
            // System.out.println("Input next value");
            long x = sc.nextLong();
            a.add(x);
        }

        Collections.sort(a);

        Set<Long> answerset = new HashSet<Long>();
        int noneedtoadd = 0;
        for (Long i: a)
        {
            if ((i * k > 1000000000) && (i % k != 0))
            {
                noneedtoadd++;
            }
            else if (k > i || i % k != 0 || !answerset.contains(i/k))  // Add it in any of these cases   
            {
                answerset.add(i);
            }
        }
        System.out.println(answerset.size() + noneedtoadd);
    }
}
