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 double pi = 4 * atan((long double)1);
const long long mod = 1e9 + 7;
const long long inf = 1e9;
const long long llinf = 1e18;
const long long nax = 0;
long long n, k;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> k;
  vector<long long> arr(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
  }
  sort(arr.begin(), arr.end());
  set<long long> s;
  for (int i = 0; i < n; ++i) {
    if (arr[i] % k != 0) {
      s.insert(arr[i]);
      continue;
    }
    if (s.count(arr[i] / k)) continue;
    s.insert(arr[i]);
  }
  cout << s.size() << '\n';
}
