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 maxint = -1u >> 1;
const double pi = 3.14159265358979323;
const double eps = 1e-8;
int n, k, a[100100];
set<long long> vis;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = (0); i < (n); i++) scanf("%d", &a[i]);
  sort(a, a + n);
  int ans = 0;
  for (int i = (0); i < (n); i++) {
    if (vis.find(a[i]) == vis.end()) {
      ans++;
      vis.insert(1LL * a[i] * k);
    } else
      continue;
  }
  printf("%d\n", ans);
  return 0;
}
