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;

public class freeSet {
    public static void main(String[]args) throws IOException{
        BufferedReader imput=new BufferedReader(new InputStreamReader(System.in));
        String[] arreglo=imput.readLine().split(" ");
        int n=Integer.parseInt(arreglo[0]);
        Long k=Long.parseLong(arreglo[1]);
        arreglo=imput.readLine().split(" ");
        Long[] numeros=new Long[n];
        Long[] resultado=new Long[n];
        for(int i =0;i<n;i++){
            numeros[i]=Long.parseLong(arreglo[i]);
            resultado[i]=(long) 0;
        }
        int i=0;
        int contador=0;
        Arrays.sort(numeros);
        while(i<n){
            if(resultado[i]==0){
                int r=Arrays.binarySearch(numeros,numeros[i]*k);
                contador++;
                if (r>0){
                    resultado[r]=(long) 1.0;
                }
            }
            i++;
        }
        System.out.println(contador);
    }
}
