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;
using ll = long long;
using ii = pair<int, int>;
void in(int &x);
const int N = 2e5;
int n, k;
void work() {
  in(n);
  in(k);
  vector<int> v(n);
  int sol = 0;
  set<int> s;
  for (int i = 0; i < n; i++) {
    in(v[i]);
    if (v[i] % k != 0) {
      sol++;
      s.insert(v[i]);
    }
  }
  sort(v.begin(), v.end());
  for (int i = 0; i < n; i++) {
    if (v[i] % k == 0) {
      if (s.find(v[i] / k) == s.end()) {
        sol++;
        s.insert(v[i]);
      }
    }
  }
  printf("%d\n", sol);
  return;
}
int main() {
  work();
  return 0;
}
void in(int &x) {
  bool neg = false;
  register int c;
  x = 0;
  c = getchar();
  if (c == '-') {
    neg = true;
    c = getchar();
  }
  for (; c > 47 && c < 58; c = getchar()) x = (x << 1) + (x << 3) + c - 48;
  if (neg) x *= -1;
}
