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;
const int mxN = 5e4 + 1;
int main() {
  set<long long> s;
  long long n, k, x;
  cin >> n >> k;
  while (n--) {
    cin >> x;
    s.insert(x);
  }
  long long ans = 0;
  while (!s.empty()) {
    long long a = *s.begin();
    long long add = 0;
    while (s.count(a)) {
      add++;
      s.erase(a);
      a *= k;
    }
    ans += (add + 1) / 2;
  }
  cout << ans;
}
