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 a, i, b, n, k, mas[100005];
set<long long> s;
int main() {
  cin >> n;
  cin >> k;
  for (i = 0; i < n; i++) {
    cin >> mas[i];
  }
  sort(mas, mas + n);
  s.insert(mas[0]);
  for (i = 1; i < n; i++) {
    if (mas[i] % k != 0) {
      s.insert(mas[i]);
    } else {
      a = s.size();
      s.insert(mas[i] / k);
      b = s.size();
      if (a != b) {
        s.erase(mas[i] / k);
        s.insert(mas[i]);
      }
    }
  }
  cout << s.size();
}
