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() {
  long long int x, k;
  while (cin >> x >> k) {
    vector<long long int> ar;
    for (long long int i = 0; i < x; i++) {
      long long int num;
      cin >> num;
      ar.push_back(num);
    }
    sort(ar.begin(), ar.end());
    map<long long int, long long int> lists;
    for (long long int i = 0; i < ar.size(); i++) {
      if (ar[i] % k != 0) {
        lists[ar[i]] = 1;
      } else {
        if (!lists.count((ar[i] / k))) {
          lists[ar[i]] = 1;
        }
      }
    }
    cout << lists.size() << endl;
  }
  return 0;
}
