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;
void read(long long a = 0) {
  freopen("in", "r", stdin);
  if (a) freopen("out", "w", stdout);
}
long long a[100009];
map<long long, long long> vis, here;
int main() {
  long long n, k;
  cin >> n >> k;
  if (k == 1) {
    return cout << n, 0;
  }
  for (int i = 0; i < n; i++) cin >> a[i], here[a[i]] = 1;
  sort(a, a + n);
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    if (!vis[a[i]]) {
      long long tmp = 0;
      long long x = a[i];
      while (here[x]) {
        vis[x] = 1;
        tmp++;
        x *= k;
      }
      ans += tmp / 2 + (tmp & 1);
    }
  }
  cout << ans;
}
