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;
struct coo {
  long long a, b, c, d;
};
bool comp(struct coo a, struct coo b) { return a.a < b.a; }
int bin_srch(vector<long long> &a, long long n, int h) {
  int l = 0;
  int mid;
  while (l <= h) {
    mid = (l + h) / 2;
    if (a[mid] > n) {
      h = mid - 1;
      continue;
    }
    if (a[mid] < n) {
      l = mid + 1;
      continue;
    }
    return mid;
  }
  return (l + h + 1) / 2;
}
int main() {
  int n, m;
  int i, j;
  int x;
  int t;
  cin >> n;
  long long k;
  cin >> k;
  vector<long long> v(n + 1);
  v[n] = 998877665544332211;
  for (i = 0; i < n; i++) {
    cin >> v[i];
  }
  sort(v.begin(), v.end());
  int count = n;
  if (k == 1) {
    cout << n << endl;
    return 0;
  }
  for (i = 0; i < n; i++) {
    int ind;
    if (v[i] != -1 && (ind = bin_srch(v, v[i] * k, n)) < n &&
        v[ind] == (v[i] * k)) {
      count--;
      v[ind] = -1;
    }
  }
  cout << (count) << endl;
  return 0;
}
