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;
int n, k;
int a[111111];
bool b[111111];
int binSearch(int x) {
  int l = 0, r = n - 1;
  while (l <= r) {
    int m = (l + r) / 2;
    if (a[m] == x) return m;
    if (a[m] > x)
      r = m - 1;
    else
      l = m + 1;
  }
  return -1;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = true;
  }
  sort(a, a + n);
  int ans = 0;
  for (int i = n - 1; i >= 0; i--)
    if (b[i]) {
      ans++;
      if (a[i] % k == 0) {
        int j = binSearch(a[i] / k);
        if (j != -1) b[j] = false;
      }
    }
  cout << ans << endl;
  return 0;
}
