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;
long long s[100010];
set<long long> x;
int main() {
  long long n, k;
  while (cin >> n >> k) {
    x.clear();
    for (int i = 1; i <= n; i++) {
      cin >> s[i];
      x.insert(s[i]);
    }
    if (k == 1) {
      cout << n << endl;
      continue;
    }
    sort(s + 1, s + 1 + n);
    int ans = 0;
    for (int i = 1; i <= n; i++) {
      long long ss = s[i];
      int cnt = 0;
      while (x.count(ss)) {
        x.erase(ss);
        ss *= k;
        ++cnt;
      }
      ans += (cnt + 1) / 2;
    }
    cout << ans << endl;
  }
  return 0;
}
