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 int MOD = 1e9 + 7;
const double EPS = 1e-9;
const int MXX = 2e5 + 5;
int a[MXX];
int main() {
  int tc;
  long long int n, k;
  cin >> n >> k;
  map<long long int, long long int> mp;
  for (int i = (0); i < (n); i++) {
    cin >> a[i];
    mp[a[i]]++;
  }
  sort(a, a + n);
  if (k == 1) return cout << n << '\n', 0;
  for (int i = (0); i < (n); i++) {
    if (!mp[a[i]]) continue;
    if (mp[k * a[i]]) mp[k * a[i]]--;
  }
  long long int ans = 0;
  for (int i = (0); i < (n); i++)
    if (mp[a[i]]) ans++;
  cout << ans << '\n';
  return 0;
}
