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.HashSet;

public class kMultipleFreeSet {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] nm = br.readLine().split(" ");
		int n = Integer.parseInt(nm[0]); 
		long m = Long.parseLong(nm[1]);
		String[] ar = br.readLine().split(" ");
		HashSet	<Long> hs = new HashSet<>();
		for (int i = 0; i < n; i++) {
			hs.add(Long.parseLong(ar[i]));
		}
		long[] nar = new long[n];
		
		boolean[] vis = new boolean[n];
		for (int i = 0; i < n; i++) {
			nar[i] = Long.parseLong(ar[i])*m;
		}
		Arrays.sort(nar);
		int x = n;
		if(m > 1) {
			for (int i = 0; i < n; i++) {
				if(hs.contains((long)nar[i])) {
					x--;
					hs.remove((long)nar[i]*m);
				}
			}
		}
		System.out.println(x);
	}
}
