#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long power(long long base, long long exp);
void solve() {
  long long n;
  cin >> n;
  long long k;
  cin >> k;
  vector<long long> arr(n, 0);
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  sort((arr).begin(), (arr).end());
  set<long long> ans;
  for (auto i : arr) {
    if (i % k == 0) {
      if (ans.count(i / k) == 0) {
        ans.insert(i);
      }
    } else {
      ans.insert(i);
    }
  }
  cout << ans.size() << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
long long power(long long base, long long exp) {
  base %= 1000000007;
  long long result = 1;
  while (exp > 0) {
    if (exp & 1) result = ((long long)result * base) % 1000000007;
    base = ((long long)base * base) % 1000000007;
    exp >>= 1;
  }
  return result;
}

### Prompt

Please create a solution in cpp 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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long power(long long base, long long exp);
void solve() {
  long long n;
  cin >> n;
  long long k;
  cin >> k;
  vector<long long> arr(n, 0);
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  sort((arr).begin(), (arr).end());
  set<long long> ans;
  for (auto i : arr) {
    if (i % k == 0) {
      if (ans.count(i / k) == 0) {
        ans.insert(i);
      }
    } else {
      ans.insert(i);
    }
  }
  cout << ans.size() << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
long long power(long long base, long long exp) {
  base %= 1000000007;
  long long result = 1;
  while (exp > 0) {
    if (exp & 1) result = ((long long)result * base) % 1000000007;
    base = ((long long)base * base) % 1000000007;
    exp >>= 1;
  }
  return result;
}

```