#include <bits/stdc++.h>
using namespace std;
int a[100009], n;
set<int> S;
int f(int x, int k) {
  S.erase(x);
  if (a[n] / x >= k && S.find(x * k) != S.end()) return f(x * k, k) + 1;
  return 1;
}
int main() {
  int i, j, k, s = 0;
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    S.insert(a[i]);
  }
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; i++)
    if (S.find(a[i]) != S.end()) {
      int t = f(a[i], k);
      s += t / 2 + t % 2;
    }
  printf("%d\n", s);
  return 0;
}

### Prompt

Your task is to create 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;
int a[100009], n;
set<int> S;
int f(int x, int k) {
  S.erase(x);
  if (a[n] / x >= k && S.find(x * k) != S.end()) return f(x * k, k) + 1;
  return 1;
}
int main() {
  int i, j, k, s = 0;
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    S.insert(a[i]);
  }
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; i++)
    if (S.find(a[i]) != S.end()) {
      int t = f(a[i], k);
      s += t / 2 + t % 2;
    }
  printf("%d\n", s);
  return 0;
}

```