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(false);
  cin.tie(NULL);
  int t = 1;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    set<long long int> s;
    map<long long int, bool> cnt;
    long long int temp;
    for (int i = 0; i < n; i++) {
      cin >> temp;
      s.insert(temp);
      cnt[temp] = 1;
    }
    int ans = 0;
    while (!s.empty()) {
      auto it = s.begin();
      vector<int> rub;
      temp = *it;
      rub.push_back(temp);
      while (cnt[temp * k] == 1 && k != 1) {
        rub.push_back(temp * k);
        temp *= k;
      }
      int size = rub.size();
      for (int i = 0; i < size; i++) s.erase(rub[i]);
      ans += (ceil((size + 0.0) / 2));
    }
    cout << ans;
  }
}
