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}.
#include <bits/stdc++.h>
using namespace std;
int n, k;
vector<int> numbers;
vector<int> s;
int maximo = 0;
void backtracking(int len, int current) {
  if (current < n) {
    int currentNumber = numbers[current];
    if ((currentNumber % k) == 0) {
      if (find(s.begin(), s.end(), (currentNumber / k)) != s.end()) {
        backtracking(len, current + 1);
        return;
      }
    }
    s.push_back(currentNumber);
    backtracking(len + 1, current + 1);
    s.pop_back();
  } else if (len > maximo) {
    maximo = len;
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  int x;
  for (int i = 0; i < n; i++) {
    cin >> x;
    numbers.push_back(x);
  }
  sort(numbers.begin(), numbers.end());
  backtracking(0, 0);
  cout << maximo;
}
