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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class C {
	
	public static void main(String [] args){
		Scanner cin = new Scanner(System.in);
		PrintWriter cout = new PrintWriter(System.out);
		int N = cin.nextInt(), k = cin.nextInt();
		int []a = new int[N];
		for (int i=0;i<N;++i)a[i] = cin.nextInt();
		Arrays.sort(a);
		if (k == 1){
			cout.println(N);
			cout.flush();
			return;
		}
		boolean []used = new boolean[N];
		for (int i=N-1;i>=0;--i)if (a[i] % k == 0 && !used[i]){
			int ind = Arrays.binarySearch(a, a[i]/k);
			if (ind >= 0)used[ind] = true;
		}
		int cnt = 0;
		for (int i=0;i<N;++i)cnt += used[i]?0:1;
		cout.println(cnt);
		cout.flush();
	}

}