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, m, a;
  cin >> n >> m;
  map<long long, long long> mp;
  while (n--) {
    cin >> a;
    mp[a] = 1;
  }
  if (m == 1) return cout << mp.size() << endl, 0;
  for (auto i : mp) {
    if (i.second == 0 || mp.find(i.first * m) == mp.end()) continue;
    mp[i.first * m] = 0;
  }
  long long sum = 0;
  for (auto i : mp) sum += i.second;
  cout << sum << endl;
  return 0;
}
