#include <bits/stdc++.h>
using namespace std;
long long INF = 1e9 + 7;
long long a[100005], z[100005];
bool b[100005];
long long bin(long long l, long long r, long long x) {
  long long c;
  if (l == r) {
    if (a[l] == x)
      return l;
    else
      return -1;
  }
  c = (l + r) / 2;
  if (a[c] >= x)
    return bin(l, c, x);
  else
    return bin(c + 1, r, x);
}
int main() {
  long long n, k;
  cin >> n >> k;
  long long i;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = true;
  }
  sort(a, a + n);
  for (i = 0; i < n - 1; i++) {
    z[i] = bin(i + 1, n - 1, k * a[i]);
  }
  z[n - 1] = -1;
  for (i = 0; i < n; i++)
    if (!b[i])
      continue;
    else {
      if (z[i] != -1) b[z[i]] = false;
    }
  long long k1 = 0;
  for (i = 0; i < n; i++)
    if (b[i]) k1++;
  cout << k1;
  return 0;
}

### 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;
long long INF = 1e9 + 7;
long long a[100005], z[100005];
bool b[100005];
long long bin(long long l, long long r, long long x) {
  long long c;
  if (l == r) {
    if (a[l] == x)
      return l;
    else
      return -1;
  }
  c = (l + r) / 2;
  if (a[c] >= x)
    return bin(l, c, x);
  else
    return bin(c + 1, r, x);
}
int main() {
  long long n, k;
  cin >> n >> k;
  long long i;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = true;
  }
  sort(a, a + n);
  for (i = 0; i < n - 1; i++) {
    z[i] = bin(i + 1, n - 1, k * a[i]);
  }
  z[n - 1] = -1;
  for (i = 0; i < n; i++)
    if (!b[i])
      continue;
    else {
      if (z[i] != -1) b[z[i]] = false;
    }
  long long k1 = 0;
  for (i = 0; i < n; i++)
    if (b[i]) k1++;
  cout << k1;
  return 0;
}

```