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 inf = (int)1e9;
const double EPS = 1e-9, INF = 1e12;
int n, k;
bool u[100000];
long long a[100000];
int main() {
  cin >> n >> k;
  for (int i = 0; i < (int)n; i++) cin >> a[i];
  sort(a, a + n);
  int ans = 0;
  for (int i = 0; i < (int)n; i++)
    if (!u[i]) {
      int nx, p = i, c = 1;
      u[i] = 1;
      while ((nx = lower_bound(a + p + 1, a + n, k * a[p]) - a) < n) {
        if (a[nx] != k * a[p]) break;
        c++;
        u[p = nx] = 1;
      }
      ans += (1 + c) / 2;
    }
  cout << ans << endl;
  return 0;
}
