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}.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int no_of_elements, k;
  scanf("%d %d", &no_of_elements, &k);
  vector<int> element(no_of_elements);
  for (int i = 0; i < no_of_elements; i++) scanf("%d", &element[i]);
  sort((element).begin(), (element).end());
  int set_size = 0;
  vector<int> crossed_out(no_of_elements, false);
  for (int i = 0; i < no_of_elements; i++) {
    if (!crossed_out[i]) {
      set_size++;
      if (binary_search((element).begin(), (element).end(),
                        k * 1LL * element[i])) {
        int index = lower_bound((element).begin(), (element).end(),
                                k * 1LL * element[i]) -
                    element.begin();
        crossed_out[index] = true;
      }
    }
  }
  printf("%d\n", set_size);
  return 0;
}
