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}.
/*w6xi*/
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	@SuppressWarnings("resource")
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Map<Integer,Integer> m = new HashMap<Integer,Integer>();
		while (sc.hasNext()) {

			int n = sc.nextInt();
			int k = sc.nextInt();
			int arr[] = new int[n];
			for (int i = 0; i < arr.length; i++) {
				arr[i] = sc.nextInt();
			}
			Arrays.sort(arr);
              
			 int a=0;
			for (int i = 0; i < arr.length; i++) {
				if(arr[i]%k!=0|m.get(arr[i]/k)==null){
					m.put(arr[i], 1);
					a++;
				}
			}System.out.println(a);
		}
	}

}
