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() {
  ios_base::sync_with_stdio(0);
  int n, k;
  cin >> n >> k;
  if (k == 1) {
    cout << n;
    return 0;
  }
  vector<int> T(n);
  for (int i = (0); i <= ((int)(T).size() - 1); ++i) cin >> T[i];
  sort(T.begin(), T.end());
  vector<bool> vis(n, 0);
  int ans = 0;
  for (int i = (0); i <= ((int)(T).size() - 1); ++i)
    if (!vis[i]) {
      int v = i, cnt = 1;
      vis[i] = 1;
      while (binary_search(T.begin(), T.end(), ((long long int)k) * T[v])) {
        v = lower_bound(T.begin(), T.end(), ((long long int)k) * T[v]) -
            T.begin();
        cnt++;
        vis[v] = 1;
      }
      ans += (cnt + 1) / 2;
    }
  cout << ans;
  return 0;
}
