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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n, k;
  cin >> n >> k;
  if (k == 1) {
    cout << n;
    return 0;
  }
  if (n == 1) {
    cout << 1;
    return 0;
  }
  set<long long int> s;
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    s.insert(x);
  }
  for (auto it = s.begin(); it != s.end(); it++) {
    long long int t = *it;
    if (s.find(t * k) != s.end()) {
      s.erase(s.find(t * k));
    }
  }
  int ans = s.size();
  cout << ans;
}
