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 Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        String[] ins = br.readLine().trim().split(" ");
        int n = Integer.parseInt(ins[0]);
        int k = Integer.parseInt(ins[1]);
        ins = br.readLine().trim().split(" ");
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = Integer.parseInt(ins[i]);
        Arrays.sort(arr);
        HashSet<Integer> hs = new HashSet<Integer>();
        int res = 0;
        for (int i = 0; i < n; i++) {
            if(arr[i] % k != 0 || !hs.contains(arr[i]/k)) {
                res++;
                hs.add(arr[i]);
            }
        }
        out.write(res+"\n");
        out.flush();
    }
}
