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 n, k, a[100100], ans;
bool used[100100];
map<int, bool> m;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i], m[a[i]] = true;
  sort(a, a + n);
  int mx = a[n - 1];
  for (int i = 0; i < n; i++) {
    if (!used[i]) {
      used[i] = 1;
      int l = 1;
      long long p = 1ll * k * a[i];
      while (p <= mx) {
        int j = lower_bound(a + i, a + n, p) - a;
        if (j > i && j < n && a[j] == p) {
          l++;
          used[j] = 1;
          p *= k;
        } else
          break;
      }
      ans += (l + 1) / 2;
    }
  }
  cout << ans;
  return 0;
}
