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.ArrayList;
import java.util.Arrays;
import java.util.Hashtable;
import java.util.Scanner;


public class f {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		Hashtable<Long, Boolean> d = new Hashtable<Long, Boolean>();
		int n = in.nextInt(), k = in.nextInt(), size = 0, a[] = new int[n];
		for (int i = 0; i < n; i++) a[i] = in.nextInt();
		Arrays.sort(a);
		for (int i = 0; i < n; i++) {
			long x = a[i];
			if (!d.containsKey(x)) {
				d.put(x * k, true);
				size++;
			}
		}
		System.out.println(size);
	}

}

  	 		   							  		 	  	 	