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 = 200002;
long long h[maxn];
int n, k;
int cmp(long long a, long long b) { return a <= b ? 1 : 0; }
int main() {
  while (scanf("%d%d", &n, &k) != EOF) {
    int i, j;
    set<long long> s;
    s.clear();
    for (i = 0; i < n; i++) {
      cin >> h[i];
    }
    sort(h, h + n, cmp);
    int cnt = 0;
    for (i = 0; i < n; i++) {
      if (s.count(h[i]) == 0) {
        cnt++;
        s.insert(h[i] * k);
      }
    }
    cout << cnt << endl;
  }
  return 0;
}
