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.util.Arrays;
public class Main {

	
	public static int	Busca(int[] input, int value,int tam){

	    if(tam == 0){return 0;}

	    
	    int left=0;
	    int right=(tam - 1);

	    while(left + 1 < right){
	        int mid = (left + right) / 2;
	        if(input[mid] == value){return 1;}
	        else if(value < input[mid]){right = mid;}
	        else if(input[mid] < value){left = mid;}
	    }
	    if(input[left] == value || input[right] == value){return 1;}

	    return 0;
	}

   
    
	public static void main(String[] args) {
		
		int n=0;
		int k=0;
		Scanner datos = new Scanner(System.in); 
		StringTokenizer tk = new StringTokenizer(datos.nextLine());
		n=Integer.parseInt(tk.nextToken());
		k=Integer.parseInt(tk.nextToken());
		StringTokenizer tk1 = new StringTokenizer(datos.nextLine());
	    int[] ar = new int[n];
	    
	    for(int  p = 0; p < n; p++)
	    {
	    	ar[p]=Integer.parseInt(tk1.nextToken());
	    }
	    Arrays.sort(ar);
	   
	   int[] lista = new int[n] ;
	
        int w=0;
	    for(int p = 0; p < n; p++){
	       
	    	if(ar[p] % k != 0){
	        	lista[w]=ar[p];
	        	w++;
	        }
	        else{
	        	
	            int divisor = ar[p] / k;
	            if ( Busca(lista,divisor,w)==0)
	            {
	            	lista[w]=ar[p];
		        	w++;
	            }
	            	
	          
	        }
	       
	    }

	    System.out.println(w);



	}

}
