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::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k;
  cin >> (n);
  cin >> (k);
  set<long long> s;
  long long ar[n + 1];
  for (long long i = 1; i <= n; i++) cin >> (ar[i]);
  sort(ar + 1, ar + n + 1);
  for (long long i = 1; i <= n; i++) {
    long long x = ar[i];
    if (x % k != 0)
      s.insert(x);
    else if (!s.count(x / k)) {
      s.insert(x);
    }
  }
  cout << (s.size());
  cout << ("\n");
}
