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;
import java.util.TreeSet;


public class KMultipleFreeSet {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader teclado = new BufferedReader(new InputStreamReader(System.in));
		String [] data = teclado.readLine().split(" ");
		int n = Integer.parseInt(data[0]);
		int k = Integer.parseInt(data[1]);
		
		TreeSet<Long> input = new TreeSet<Long>();
		
		long [] numbers = new long[n];
		data = teclado.readLine().split(" ");
		for (int i = 0; i<n; ++i)
		{
			numbers[i] = Long.parseLong(data[i]);
			input.add(numbers[i]);
		}
		
		if (k != 1)
		{
			Arrays.sort(numbers);
			
			int total = 0;
			for (int i = 0; i<n; ++i)
			{
				long number = numbers[i];
				if (input.contains(number))
				{
					boolean swap = true;
					while (number <= numbers[n-1])
					{
						if (!input.contains(number)) break;
						if (swap)
						{
							++total;
						}
						input.remove(number);
						number*=k;
						swap = !swap;
					}
				}
			}
			System.out.println(total);
		}
		else
		{
			System.out.println(n);
		}
	}
	

}
