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 n, k;
long long A[100001], B[100001];
bool C[100001];
int bb(long long a) {
  int i = 0, f = n, m;
  while (f - i > 1) {
    m = (i + f) / 2;
    if (A[m] <= a)
      i = m;
    else
      f = m;
  }
  return i;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> A[i];
  }
  if (k == 1) {
    set<int> S;
    for (int i = 0; i < n; i++) {
      S.insert(A[i]);
    }
    cout << S.size() << endl;
    return 0;
  }
  sort(&A[0], &A[0] + n);
  for (int i = 0; i < n; i++) {
    int pos = bb(A[i] * k);
    if (A[pos] == A[i] * k) {
      C[i] = true;
      B[pos] = B[i] + 1;
    }
  }
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (C[i] == false) {
      ans += (B[i] + 2) / 2;
    }
  }
  cout << ans << endl;
  return 0;
}
