#include <bits/stdc++.h>
using namespace std;
set<long long> S;
int A[100010];
long long K;
int solve(long long x) {
  if (x % K) return 1;
  if (S.find(x / K) != S.end()) return 1 + solve(x / K);
  return 1;
}
int main() {
  int N;
  cin >> N >> K;
  for (int i = 0; i < (N); ++i) cin >> A[i], S.insert(A[i]);
  if (K == 1) {
    cout << N << endl;
    return 0;
  }
  int ans = 0;
  for (int i = 0; i < (N); ++i) {
    if (S.find(K * A[i]) == S.end()) ans += ((solve(A[i]) + 1) / 2);
  }
  cout << ans << endl;
}

### 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;
set<long long> S;
int A[100010];
long long K;
int solve(long long x) {
  if (x % K) return 1;
  if (S.find(x / K) != S.end()) return 1 + solve(x / K);
  return 1;
}
int main() {
  int N;
  cin >> N >> K;
  for (int i = 0; i < (N); ++i) cin >> A[i], S.insert(A[i]);
  if (K == 1) {
    cout << N << endl;
    return 0;
  }
  int ans = 0;
  for (int i = 0; i < (N); ++i) {
    if (S.find(K * A[i]) == S.end()) ans += ((solve(A[i]) + 1) / 2);
  }
  cout << ans << endl;
}

```