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.TreeSet;


public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        String lineaUno[]  = buffer.readLine().split(" ");
        long n = Long.parseLong(lineaUno[0]);
        long k = Long.parseLong(lineaUno[1]);
        TreeSet<Long> setOrd = new TreeSet<Long>();
        String lineaDos[]  = buffer.readLine().split(" ");
        for (int i = 0; i < n; i++) {
            setOrd.add(Long.parseLong(lineaDos[i]));            
        }
        if(k != 1)
        {
            int cont = 0;
            while (!setOrd.isEmpty()) {
                long num = setOrd.pollFirst();          
                setOrd.remove(new Long(num*k));
                cont++;
            }
            System.out.println(cont);
        }
        else{
            System.out.println(n);
        }
    }
    
}
