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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

public class CF274A_KMultipleFreeSet {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        String[] ina = in.readLine().split(" ");
        int n = Integer.valueOf(ina[0]);
        long k = Integer.valueOf(ina[1]);
        Long[] a = new Long[n];
        ina = in.readLine().split(" ");
        for (int i = 0; i < n; i++)
            a[i] = Long.valueOf(ina[i]);
        Arrays.sort(a);
        Set<Long> set = new HashSet<Long>();
        int res = 0;
        for (int i = 0; i < n; i++) {
            if (!set.contains(a[i])) {
                res++;
                set.add(a[i] * k);
            }
        }
        out.println(res);
        out.flush();
    }
}

