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 main() {
  long long n, k;
  while (cin >> n >> k) {
    long long t[n];
    for (int i = 0; i < (int)n; i++) cin >> t[i];
    sort(t, t + n);
    set<long long> S;
    long long cnt = 0;
    for (int i = 0; i < (int)n; i++) {
      if (S.count(t[i])) continue;
      cnt++;
      S.insert(t[i] * k);
    }
    cout << cnt << endl;
  }
  return 0;
}
