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 a[100000 + 10], b[100000 + 10];
bool f(int x, int y) {
  int l = 1, r = x, mid, ans = 0;
  while (l <= r) {
    mid = (l + r) >> 1;
    if (b[mid] < y)
      l = mid + 1;
    else {
      ans = mid;
      r = mid - 1;
    }
  }
  if (b[ans] == y)
    return 1;
  else
    return 0;
}
int main() {
  int n, i;
  long long k;
  while (cin >> n >> k) {
    for (i = 1; i <= n; i++) cin >> a[i];
    sort(a + 1, a + 1 + n);
    int cnt = 0;
    for (i = 1; i <= n; i++) {
      if (a[i] % k)
        b[++cnt] = a[i];
      else {
        if (f(cnt, a[i] / k))
          continue;
        else
          b[++cnt] = a[i];
      }
    }
    cout << cnt << endl;
  }
  return 0;
}
