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.*;
import java.util.*;
import java.math.*;
import java.text.*;

public class Main {

    Scanner cin = new Scanner(new BufferedInputStream(System.in));

    int n,k;
    BigInteger ar[],p;
    boolean flag[];
    void run(){
        n = cin.nextInt();
        k = cin.nextInt();
        ar = new BigInteger[n+1];
        flag = new boolean[n+1];
        for(int i = 0; i < n; i++){
            ar[i] = cin.nextBigInteger();
            flag[i] = false;
        }
        Arrays.sort(ar,0,n);
        int ans = n;
        for(int i = 0; i < n; i++){
            if(!flag[i]){
                p = ar[i].multiply(BigInteger.valueOf(k));
                int left = i + 1;
                int right = n - 1;
                while(left <= right){
                    int mid = (left + right)/2;
                    if(ar[mid].compareTo(p) < 0)
                        left = mid + 1;
                    else if(ar[mid].compareTo(p) > 0)
                        right = mid - 1;
                    else{
                        flag[mid] = true;
                        ans--;
                        break;
                    }
                }
            }
        }
        System.out.println(ans);
    }
    public static void main(String[] args) {
        new Main().run();

    }

}
