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, answer;
vector<long long> a, visited, p;
long long BinarySearch(long long search) {
  long long l = 0;
  long long r = n - 1;
  long long middle = (l + r) / 2;
  while (l < r) {
    if (a[middle] >= search) {
      r = middle;
    } else {
      l = middle + 1;
    }
    middle = (l + r) / 2;
  }
  if (a[middle] != search) {
    return n;
  }
  return middle;
}
int main() {
  scanf("%lld %lld", &n, &k);
  a.resize(n);
  p.resize(n + 1);
  fill(p.begin(), p.end(), n);
  for (int i = 0; i < n; i++) {
    scanf("%lld", &a[i]);
  }
  sort(a.begin(), a.end());
  for (int i = 0; i < n; i++) {
    p[i] = BinarySearch(a[i] * k);
  }
  visited.resize(n + 1);
  for (int i = 0; i < n; i++) {
    if (!visited[i]) {
      answer++;
      visited[i] = 1;
      visited[p[i]] = 1;
    }
  }
  printf("%lld\n", answer);
  return 0;
}
