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;
const int maxn = 100010;
bool vis[maxn];
long long num[maxn];
int main() {
  int n;
  long long k;
  scanf("%d%lld", &n, &k);
  for (int i = 1; i <= n; ++i) {
    scanf("%lld", &num[i]);
  }
  sort(num + 1, num + n + 1);
  memset(vis, false, sizeof(vis));
  int ans = n;
  for (int i = 1; i <= n; ++i) {
    if (vis[i]) continue;
    int left = i + 1, right = n;
    long long temp = num[i] * k;
    while (left <= right) {
      int mid = (left + right) >> 1;
      if (num[mid] == temp) {
        vis[mid] = true;
        ans--;
        break;
      } else if (num[mid] > temp) {
        right = mid - 1;
      } else {
        left = mid + 1;
      }
    }
  }
  printf("%d\n", ans);
  return 0;
}
