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() {
  long long n, i, j, k, ans = 0, m, l;
  cin >> n >> m;
  vector<long long> arr(n);
  map<long long, long long> mp, vis;
  set<long long> s;
  set<long long>::iterator it;
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) {
    k = arr[i];
    s.insert(k);
    mp[k]++;
  }
  if (m == 1)
    ans = s.size();
  else {
    vector<long long> brr;
    for (it = s.begin(); it != s.end(); it++) brr.push_back(*it);
    for (i = 0; i < brr.size(); i++) {
      if (!vis[brr[i]]) {
        vector<long long> temp;
        for (j = brr[i]; mp[j]; vis[j] = 1, j *= m) temp.push_back(mp[j]);
        long long a = temp[0], b = 0;
        if (temp.size() > 1) {
          b = temp[1];
          for (l = 2; l < temp.size(); l++) {
            if (l % 2 == 0)
              a += temp[l];
            else
              b += temp[l];
          }
        }
        ans += max(a, b);
      }
    }
  }
  cout << ans << endl;
  return 0;
}
