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 n, k, p, a, b, x, y, i, m[100005];
map<int, int> mp;
int main() {
  cin >> n >> k;
  while (i < n) {
    cin >> m[i];
    i++;
  }
  i = 0;
  sort(m, m + n);
  while (i < n) {
    if (m[i] % k != 0 || (m[i] % k == 0 && mp[m[i] / k] == 0)) {
      mp[m[i]]++;
      p++;
    }
    i++;
  }
  cout << p;
}
