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.Scanner;
import java.util.TreeMap;

public class Solution {

  public static void main(String[] args) throws Exception {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    long k = in.nextInt();
    TreeMap<Long, Long> map = new TreeMap<Long, Long>();
    for (int i = 0; i < n; i++) {
      long x = in.nextInt();
      if (!map.containsKey(x))
        map.put(x, 1L);
      else
        map.put(x, map.get(x) + 1);
    }
    int count = 0;
    while (!map.isEmpty()) {
      long x = map.firstKey();
      long l = map.remove(x), r = 0, i = 1;
      while (map.containsKey(x * k)) {
        x = x * k;
        if (i == 0)
          l += map.remove(x);
        else
          r += map.remove(x);
        i = 1 - i;
      }
      count += Math.max(l, r);
    }
    System.out.println(count);
  }
}
