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 A[1 << 20];
int B[1 << 20];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  int i;
  for (i = (0); i < (n); ++i) {
    int a;
    scanf("%d", &a);
    A[i] = a;
  }
  sort(A, A + n);
  int res = 0;
  memset(B, 0, sizeof(B));
  for (i = (0); i < (n); ++i)
    if (B[i] == 0) {
      long long a = A[i];
      int cnt = 0;
      while (true) {
        int pos = lower_bound(A, A + n, a) - A;
        if (pos == n || A[pos] != a || B[pos] != 0) break;
        B[pos] = 1;
        ++cnt;
        a *= k;
      }
      res += (cnt + 1) >> 1;
    }
  printf("%d\n", res);
  return 0;
};
