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 main() {
  long long n, k;
  cin >> n >> k;
  map<long long, int> m;
  long long a[n + 1];
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + n + 1);
  long long x = 0;
  for (int i = 1; i <= n; ++i) {
    if (m[a[i]] < 1) m[a[i]] = 1;
    long long p = a[i] * k;
    if (m[a[i]] == 1)
      m[p] = m[a[i]] + 1;
    else
      m[p] = m[a[i]] - 1;
    if (m[a[i]] == 1) x++;
  }
  int r = max(x, n - x);
  cout << r << endl;
}
