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;
bool binary(vector<int>& vec, int lenght, long long int val) {
  int left = 0, right = lenght - 1, mid = (left + right) / 2;
  while (left <= right) {
    if (vec[mid] == val) {
      vec[mid] = 0;
      return true;
    } else if (vec[mid] > val) {
      right = mid - 1;
      mid = (left + right) / 2;
    } else {
      left = mid + 1;
      mid = (left + right) / 2;
    }
  }
  return false;
}
int main() {
  int n, i, x, cnt = 0;
  long long int k, f;
  cin >> n >> k;
  vector<int> vec;
  for (i = 0; i < n; i++) {
    scanf("%i", &x);
    vec.push_back(x);
  }
  sort(vec.begin(), vec.end());
  i = 0;
  f = vec[i] * k;
  while (f <= vec[vec.size() - 1] && i < vec.size() - 1) {
    f = vec[i] * k;
    if (binary(vec, vec.size(), f) && vec[i] != 0) cnt++;
    i++;
  }
  cout << n - cnt;
  return 0;
}
