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;
void solve() {
  long long int n, k;
  scanf("%lli%lli", &n, &k);
  vector<long long int> a(n);
  set<long long int> k_set;
  for (int(i) = 0; i < n; i++) scanf("%lli", &a[i]);
  sort(a.rbegin(), a.rend());
  for (int(i) = 0; i < n; i++) {
    bool exist = k_set.find(a[i] * k) != k_set.end();
    if (!exist) k_set.insert(a[i]);
  }
  cout << k_set.size() << endl;
}
int main() {
  solve();
  return 0;
}
