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 inp[100003], ans = 0;
map<long long, long long> vis;
map<long long, bool> used;
int main() {
  long long n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> inp[i];
  sort(inp, inp + n);
  for (int i = n - 1; i >= 0; i--) {
    vis[inp[i]]++;
    if (!used[inp[i] * k])
      ans++, used[inp[i]] = true;
    else if (vis[inp[i]] - 1 == vis[inp[i] * k])
      ans += vis[inp[i]], ans -= vis[inp[i] * k], used[inp[i]] = true,
                                                  used[inp[i] * k] = false;
    else if (vis[inp[i]] - 1 > vis[inp[i] * k])
      ans++;
  }
  cout << ans << endl;
}
