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;
const int MAXN = 1000000005;
set<int> s;
map<int, bool> M;
int n, k, x;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> x;
    M[x] = 1;
    if (k != 1)
      while (x % k == 0) x /= k;
    s.insert(x);
  }
  if (k == 1) {
    cout << n << endl;
    return 0;
  }
  long long ax = 0;
  int ans = 0;
  for (set<int>::iterator it = s.begin(); it != s.end(); ++it) {
    ax = *it;
    int ct = 0;
    while (ax < MAXN) {
      if (M[ax] == 1) {
        ct++;
      } else {
        ans = ans + ct / 2 + ct % 2;
        ct = 0;
      }
      ax *= k;
    }
    ans = ans + ct / 2 + ct % 2;
  }
  cout << ans << "\n";
}
