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 MOD = 1e9 + 7;
const int MAX = 100010;
int n, k;
long long int v[MAX];
map<long long int, int> M, mark;
int main() {
  scanf("%d", &(n));
  scanf("%d", &(k));
  for (int i = 0, _n = (n); i < _n; ++i) {
    cin >> v[i];
    M[v[i]] = 1;
    mark[v[i]] = 1;
  }
  sort(v, v + n);
  long long int ans = n;
  for (int i = 0, _n = (n); i < _n; ++i) {
    if (M[k * 1ll * v[i]]) {
      if (mark[v[i]]) {
        ans--;
        mark[k * 1ll * v[i]] = 0;
      }
    }
  }
  cout << (k == 1 ? n : ans) << endl;
  return 0;
}
