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;
set<int> s;
set<int>::iterator it1;
map<int, int>::iterator it;
map<int, int> mp;
pair<int, int> pa;
int main() {
  int n, k;
  int ar[100008];
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
    mp[ar[i]] = 0;
  }
  s.clear();
  sort(ar, ar + n);
  for (int i = 0; i < n; i++) {
    if (ar[i] % k == 0) {
      int x = ar[i] / k;
      if (mp[x] == 0) {
        mp[ar[i]] = 1;
      }
    } else {
      mp[ar[i]] = 1;
    }
  }
  int c = 0;
  for (it = mp.begin(); it != mp.end(); it++) {
    pa = *(it);
    if (pa.second == 1) c++;
  }
  cout << c << "\n";
  return 0;
}
