#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long i, j, k, n, q, ans, t, cnt, c1, c2;
  vector<long long> v;
  unordered_map<long long, long long> m;
  cin >> n >> k;
  i = 0;
  while (i < n) {
    cin >> q;
    v.push_back(q);
    i++;
  }
  i = 0;
  cnt = 0;
  sort(v.begin(), v.end());
  while (i < n) {
    if (m[v[i]] == 0) {
      cnt++;
      m[k * v[i]]++;
    }
    i++;
  }
  cout << cnt;
  return (0);
}

### Prompt

In CPP, your task is to solve the following problem:

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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long i, j, k, n, q, ans, t, cnt, c1, c2;
  vector<long long> v;
  unordered_map<long long, long long> m;
  cin >> n >> k;
  i = 0;
  while (i < n) {
    cin >> q;
    v.push_back(q);
    i++;
  }
  i = 0;
  cnt = 0;
  sort(v.begin(), v.end());
  while (i < n) {
    if (m[v[i]] == 0) {
      cnt++;
      m[k * v[i]]++;
    }
    i++;
  }
  cout << cnt;
  return (0);
}

```