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;
priority_queue<int, vector<int>, greater<int> > Q;
const int INF = 1e9 + 9;
struct cmp {
  bool operator()(pair<int, int> const &a, pair<int, int> const &b) {
    if (a.first == b.first) return a.second > b.second;
    return a.first < b.first;
  }
};
int main() {
  int n, k;
  cin >> n >> k;
  vector<long long> v;
  map<long long, long long> m;
  for (long long i = 0; i < n; i++) {
    long long x;
    cin >> x;
    v.push_back(x);
    m[x]++;
  }
  sort(v.begin(), v.end());
  long long cnt = 0;
  for (long long i = 0; i < n; i++) {
    if (m[v[i]]) {
      cnt++;
      m[k * v[i]] = 0;
    }
  }
  cout << cnt << endl;
}
