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 Solve {
    public static void main(String[] args) throws IOException
    {
        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        String t=bf.readLine();
        String[] bb=t.trim().split("\\s+");
        int size=Integer.parseInt(bb[0]);
        int k=Integer.parseInt(bb[1]);
        int[] arr=new int[size];
        String tt=bf.readLine();
        String[] strs=tt.trim().split("\\s+");
        for(int i=0;i<size;i++)
        {
            arr[i]=Integer.parseInt(strs[i]);
        }
        Set<Integer> st=new HashSet<>();
        Arrays.sort(arr);
        for(int i=0;i<size;i++)
        {
            if(arr[i]%k==0&&!st.contains(arr[i]/k))
            {
                st.add(arr[i]);
            }
            else if(arr[i]%k!=0)
            {
                st.add(arr[i]);
            }
        }
        System.out.println(st.size());
    }
    
}
