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;
vector<long long> v, value;
const int sz = 100010;
int cowbells[sz];
set<long long> S;
map<long long, vector<long long> > H;
map<long long, vector<long long> >::iterator it;
int main() {
  int n;
  long long k, elm;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> elm;
    v.push_back(elm);
    S.insert(elm);
  }
  sort(v.begin(), v.end());
  for (int i = 0; i < v.size(); ++i) {
    if (S.find(v[i]) != S.end()) {
      value.clear();
      value.push_back(v[i]);
      elm = v[i];
      S.erase(v[i]);
      while (S.find(elm * k) != S.end()) {
        value.push_back(elm * k);
        S.erase(elm * k);
        elm = elm * k;
      }
      H[v[i]] = value;
    }
  }
  int res = 0;
  for (it = H.begin(); it != H.end(); ++it) {
    elm = it->second.size();
    elm = (elm + 1) / 2;
    res += elm;
  }
  cout << res;
  return 0;
}
