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;
map<long long, bool> mp;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  long long m, n, b, c, d, i, j, k, x, y, z, l, q, r;
  string s1, s2, s3, s4;
  long long cnt = 0, ans = 0, sum = 0;
  cin >> n;
  ;
  cin >> k;
  ;
  long long *a = new long long[n + 1]();
  for (long long i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  set<long long> st;
  for (long long i = 0; i < n; i++)
    if (a[i] % k or (a[i] % k == 0 and mp[a[i] / k] == 0))
      st.insert(a[i]), mp[a[i]] = 1;
  cout << st.size() << endl;
  return 0;
}
