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.io.*;
import java.util.*;

/**
 * User: Oleksiy Pylypenko
 * Date: 1/6/13
 * Time: 1:46 PM
 */
public class A {
    static boolean debug = !"true".equalsIgnoreCase(System.getProperty("ONLINE_JUDGE"));
    private Scanner in;
    private PrintWriter out;

    private void solve() throws IOException {
        int n = in.nextInt(), k = in.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = in.nextInt();
        Arrays.sort(a);
        Map<Long, Integer> map = new HashMap<Long, Integer>();
        for (long v : a) {
            Integer val = map.get(v);
            if (val == null) {
                val = 0;
            }
            map.remove(v);
            long r = v;
            r *= k;
            map.put(r, val + 1);
        }

        int res = 0;
        for (int cnt : map.values()) {
            res += (cnt + 1) / 2;
        }
        out.println(res);
    }

    public static void main(String[] args) throws IOException {
        new A().exec();
    }

    private void exec() {
        if (debug) {
            try {
                System.setIn(new FileInputStream(getClass().getName() + ".in"));
            } catch (FileNotFoundException e) {
                System.out.println(e);
                System.exit(1);
            }
        }
        in = new Scanner(new InputStreamReader(System.in));
        out = new PrintWriter(System.out, true);

        try {
            if (debug) {
                while (in.hasNext()) {
                    solve();
                }
            } else {
                solve();
            }
        } catch (IOException e) {
            if (debug) {
                System.out.println(e);
                System.exit(1);
            }
        } finally {
            out.close();
            in.close();
        }
    }

}
