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 long long INF = 1e17;
const long long N = 6e5 + 100;
const int MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, k;
  cin >> n >> k;
  vector<int> vec(n);
  unordered_set<long long> ss;
  for (int i = 0; i < n; i++) {
    cin >> vec[i];
    ss.insert(vec[i]);
  }
  sort(vec.begin(), vec.end());
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (!ss.count(vec[i])) continue;
    int len = 1;
    long long num = vec[i];
    while (ss.count(num * k)) {
      len++;
      num *= k;
      ss.erase(num);
    }
    ans += (len - len / 2);
  }
  cout << ans << endl;
  return 0;
}
