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;
long long int n, m, c, k, cnt, x, y, a, b, s, ans;
vector<long long int> g[1001];
queue<long long int> q;
long long int used[100001];
map<long long int, long long int> mp;
long long int d[1001];
long long int arr[1000001];
long long int INF = 1e18;
int main() {
  ios_base::sync_with_stdio(0);
  ;
  cin >> n >> m;
  for (long long int i = 1; i <= n; i++) {
    cin >> arr[i];
  }
  sort(arr + 1, arr + 1 + n);
  for (long long int i = 1; i <= n; i++) {
    if (mp[arr[i]] == 0) {
      ans++;
      mp[arr[i]]++;
      mp[arr[i] * m]++;
    }
  }
  cout << ans << endl;
}
