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;
long long n, m, len, l;
map<long long, bool> used;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  int nn[n];
  for (int i = 0; i < n && cin >> nn[i]; i++) used[nn[i]] = 1;
  for (int i = 0; i < n; i++) {
    if (!used[nn[i]]) continue;
    int cnt = 1;
    long long r = nn[i] * m, l = nn[i] / m;
    used[nn[i]] = 0;
    while (used[r]) {
      used[r] = 0;
      r *= m;
      cnt++;
    }
    if (nn[i] % m == 0)
      while (used[l]) {
        used[l] = 0;
        cnt++;
        if (l % m == 0)
          l /= m;
        else
          break;
      }
    len += cnt / 2 + cnt % 2;
  }
  cout << len;
  return 0;
}
