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.util.Arrays;
import java.util.HashMap;
import java.util.Map;

/**
 *
 * @author Donato
 */
public class KMultipleFreeSet {


    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Map<Integer, Integer> nombres;
        nombres = new HashMap<>();
        String[] linea=br.readLine().split(" ");
        int n=Integer.parseInt(linea[0]);
        int k=Integer.parseInt(linea[1]);
        int[] num=new int[n];
        int[] esta=new int[n];
        linea=br.readLine().split(" ");
        int total=0;
        for(int i=0;i<n;i++){
            num[i]=Integer.parseInt(linea[i]);
        }
        Arrays.sort(num);
        for(int i=0;i<n;i++){
            if(num[i]%k!=0){
                total++;
                nombres.put(num[i], i);
            }
            else{
                if(!nombres.containsKey(num[i]/k)){
                    total++;
                    nombres.put(num[i], i);  
                }
            }
        }
        System.out.println(total);
    }
    
}