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 mod = 655373;
int a[100005];
vector<int> v[655373];
bool invec(int n) {
  int rest = n % mod;
  for (int i = 0; i < v[rest].size(); i++)
    if (v[rest][i] == n) return 1;
  return 0;
}
int main() {
  int n, k, i, ans = 0;
  scanf("%d%d", &n, &k);
  for (i = 0; i < n; i++) scanf("%d", a + i);
  sort(a, a + n);
  for (i = 0; i < n; i++) {
    if (a[i] % k == 0 && !invec(a[i] / k))
      v[a[i] % mod].push_back(a[i]);
    else if (a[i] % k != 0)
      v[a[i] % mod].push_back(a[i]);
  }
  for (i = 0; i < mod; i++) ans += v[i].size();
  printf("%d\n", ans);
  return 0;
}
