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 n, k, v[100005], rez;
multiset<long long> s;
set<long long> nu;
multiset<pair<long long, long long> > z;
map<long long, long long> mp;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
    s.insert(v[i]);
  }
  sort(v, v + n);
  for (int i = 0; i < n; ++i) {
    int cnt = s.count(k * v[i]);
    if (v[i] % k == 0 && mp[v[i] / k] > cnt) ++cnt;
    z.insert(make_pair(cnt, v[i]));
    mp[v[i]] = cnt;
  }
  for (multiset<pair<long long, long long> >::iterator is = z.begin();
       is != z.end(); ++is) {
    if (nu.find(is->second) == nu.end()) {
      ++rez;
      nu.insert(is->second * k);
      if (is->second % k == 0) nu.insert(is->second / k);
    }
  }
  cout << rez;
  return 0;
}
