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;
int main() {
  int n;
  cin >> n;
  long long int k;
  cin >> k;
  long long int arr[n];
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  if (k == 1) {
    cout << n << "\n";
    return 0;
  }
  sort(arr, arr + n);
  unordered_map<long long, vector<int> > mp;
  long long j;
  int counts = 0;
  for (int i = 0; i < n; i++) {
    j = arr[i];
    counts = 0;
    while (j > 0 && j % k == 0) {
      j = j / k;
      counts++;
    }
    mp[j].push_back(counts);
  }
  long long int ans = 0;
  int prev = 0;
  for (auto g : mp) {
    prev = -1;
    counts = 0;
    for (auto num : g.second) {
      if (num == prev + 1 || prev == -1) {
        counts++;
        prev = num;
      } else {
        ans += ceil(counts * 1.0 / 2);
        prev = num;
        counts = 1;
      }
    }
    ans += ceil(counts * 1.0 / 2);
  }
  cout << ans << "\n";
  return 0;
}
