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;
map<long long, bool> mp;
map<long long, bool> if_calculated;
int main() {
  int n;
  long long k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    int t;
    cin >> t;
    mp[t] = 1;
  }
  int ans = 0;
  if (k == 1)
    ans = n;
  else
    for (auto i : mp) {
      long long pos = i.first;
      int num = 0;
      while (mp[pos]) {
        mp[pos] = 0;
        num++;
        pos *= k;
      }
      ans += ((num + 1) >> 1);
    }
  cout << ans << endl;
}
