#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100000;
bool muerto[MAXN + 2];
long long int a[MAXN + 2];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long int k;
  cin >> n;
  cin >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + n + 1);
  int idx = 1, resp = n;
  long long int busco;
  for (int i = 1; i <= n; i++) {
    if (muerto[i]) continue;
    busco = a[i] * k;
    idx = max(idx, i + 1);
    while (a[idx] < busco && idx <= n) idx++;
    if (a[idx] == busco) {
      muerto[idx] = true;
      resp--;
    }
  }
  cout << resp << "\n";
  return 0;
}

### Prompt

Generate a Cpp solution to 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;
const int MAXN = 100000;
bool muerto[MAXN + 2];
long long int a[MAXN + 2];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long int k;
  cin >> n;
  cin >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + n + 1);
  int idx = 1, resp = n;
  long long int busco;
  for (int i = 1; i <= n; i++) {
    if (muerto[i]) continue;
    busco = a[i] * k;
    idx = max(idx, i + 1);
    while (a[idx] < busco && idx <= n) idx++;
    if (a[idx] == busco) {
      muerto[idx] = true;
      resp--;
    }
  }
  cout << resp << "\n";
  return 0;
}

```