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 a[100010], b[1000], d[10010], p[10010];
long long mn = 1e9, mx = -1e9, ans, cnt, sm = 1, n, m;
bool ok, okk, u[1000010], uu[310][310], uk[1000010];
char ck[510][510], ch[100010];
int dx[4] = {0, 1, 0, -1}, dy[4] = {-1, 0, 1, 0};
vector<int> g[900010];
string s[1000010];
int main() {
  long long k;
  cin >> n >> k;
  map<long long, bool> mpp;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a, a + n);
  for (int i = 0; i < n; i++) {
    if (!mpp[a[i]]) {
      ans++;
      mpp[a[i] * k] = true;
    }
  }
  cout << ans;
  return 0;
}
