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 maxn = 100050;
int n, k, ans, vis[maxn];
long long a[maxn];
int main() {
  while (scanf("%d%d", &n, &k) != EOF) {
    for (int i = 1; i <= n; i++) scanf("%lld", a + i);
    if (k == 1) {
      printf("%d\n", n);
      continue;
    }
    sort(a + 1, a + n + 1);
    memset(vis, 0, sizeof(vis));
    ans = 0;
    for (int i = 1; i <= n; i++) {
      if (vis[i]) continue;
      vis[i] = 1;
      int j = i, cnt = 1;
      while (1) {
        if (a[n] / a[j] < k) break;
        int ii = lower_bound(a + 1, a + n + 1, a[j] * k) - a;
        if (a[j] * k != a[ii]) break;
        cnt++;
        j = ii;
        vis[j] = 1;
      }
      ans += (cnt + 1) / 2;
    }
    printf("%d\n", ans);
  }
  return 0;
}
