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;
long long int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  long long int arr[n];
  map<long long int, long long int> id;
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
    id[arr[i]] += 1;
  }
  for (auto it : id) {
    long long int x = it.first;
    long long int y = it.second;
    long long int num = k * x;
    if (id.find(num) != id.end() and id[num] != -1 and k != 1) {
      long long int y2 = id[num];
      if (y < y2) {
        id[it.first] = -1;
      } else {
        id[num] = -1;
      }
    }
  }
  long long int ans = 0;
  for (auto it : id) {
    if (it.second != -1) ans += it.second;
  }
  cout << max(ans, 1ll) << "\n";
  return 0;
}
