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;
void solve(istream &in, ostream &out) {
  int n, k;
  in >> n >> k;
  if (k == 1) {
    out << n << endl;
    return;
  }
  vector<int> a(n);
  map<int, bool> m;
  for (int i = 0; i < n; ++i) {
    in >> a[i];
    m[a[i]] = true;
  }
  int v = *max_element(a.begin(), a.end());
  for (auto p : m) {
    if (p.second) {
      if (p.first > 1000000000 / k) continue;
      int j = p.first * k;
      if (m.find(j) != m.end()) {
        m[j] = false;
      }
    }
  }
  out << count_if(m.begin(), m.end(), [](pair<int, bool> p) {
    return p.second;
  }) << endl;
}
int main() {
  solve(cin, cout);
  return 0;
}
