#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, k;
  cin >> n >> k;
  vector<long long> vec(n);
  for (int i = 0; i < n; ++i) cin >> vec[i];
  sort(vec.begin(), vec.end());
  vector<int> seta, setb;
  for (int i = 0; i < n; ++i) {
    if (vec[i] == -1) continue;
    auto iter = lower_bound(vec.begin(), vec.end(), vec[i] * k);
    if (iter != vec.end() && *iter == vec[i] * k) {
      seta.push_back(vec[i]);
      setb.push_back(*iter);
      *iter = -1;
    } else {
      seta.push_back(vec[i]);
      setb.push_back(vec[i]);
    }
  }
  cout << max(seta.size(), setb.size());
}

### Prompt

Develop a solution in cpp to the problem described below:

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}.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, k;
  cin >> n >> k;
  vector<long long> vec(n);
  for (int i = 0; i < n; ++i) cin >> vec[i];
  sort(vec.begin(), vec.end());
  vector<int> seta, setb;
  for (int i = 0; i < n; ++i) {
    if (vec[i] == -1) continue;
    auto iter = lower_bound(vec.begin(), vec.end(), vec[i] * k);
    if (iter != vec.end() && *iter == vec[i] * k) {
      seta.push_back(vec[i]);
      setb.push_back(*iter);
      *iter = -1;
    } else {
      seta.push_back(vec[i]);
      setb.push_back(vec[i]);
    }
  }
  cout << max(seta.size(), setb.size());
}

```