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.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String[] info = sc.nextLine().split(" ");
        int n = Integer.parseInt(info[0]);
        int k = Integer.parseInt(info[1]);
        info = sc.nextLine().split(" ");
        sc.close();

        int[] nums = new int[n];
        for (int i = 0; i < n; i++)
            nums[i] = Integer.parseInt(info[i]);
        Arrays.sort(nums);

        int max = Integer.MAX_VALUE / k;

        HashSet<Integer> remove = new HashSet<Integer>();

        int result = 0;
        for (int i = 0; i < n; i++) {
            if (!remove.contains(nums[i]))
                result++;
            if (nums[i] <= max) {
                int numk = nums[i] * k;
                if (!remove.contains(nums[i]))
                    remove.add(numk);
            }
        }

        System.out.println(result);
    }
}
