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.io.StreamTokenizer;
import java.util.Collections;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Set;

public class Round168ProblemC {

	public static void main(String[] args) {
		Reader r = new Reader();
		int n = r.nextInt();
		int k = r.nextInt();
		int result = 0;

		PriorityQueue<Integer> queue = new PriorityQueue<Integer>(n,
				Collections.reverseOrder());
		Set<Integer> set = new HashSet<Integer>();

		for (int i = 0; i < n; i++) {
			queue.add(r.nextInt());
		}

		while (!queue.isEmpty()) {
			int next = queue.poll();
			if (!set.contains(next)) {
				result++;
				if (next % k == 0) {
					set.add(next / k);
				}
			}
		}
		System.out.println(result);
	}

	static class Reader {
		StreamTokenizer in = new StreamTokenizer(new BufferedReader(
				new InputStreamReader(System.in)));

		public int nextInt() {
			try {
				in.nextToken();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return (int) in.nval;
		}

		public String nextString() {
			try {
				in.nextToken();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return in.sval;
		}
	}

}
