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.StringTokenizer;

public class Prob274A {
	public static void main(String[] Args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int x = Integer.parseInt(st.nextToken());
		long k = Integer.parseInt(st.nextToken());
		int count = x;

		if (k != 1) {
			st = new StringTokenizer(br.readLine());
			long[] arr = new long[x];
			boolean[] v = new boolean[x];
			for (int i = 0; i < x; i++)
				arr[i] = Integer.parseInt(st.nextToken());
			Arrays.sort(arr);

			for (int i = 0; i < x; i++) {
				if (arr[i] % k == 0) {
					int in = Arrays.binarySearch(arr, arr[i] / k);
					if (in >= 0 && !v[in]) {
						count--;
						v[i] = true;
					}
				}
			}
		}
		
		System.out.println(count);
	}
}