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;
int main() {
  long int quant, mul;
  scanf("%ld %ld", &quant, &mul);
  long int *nums = (long int *)calloc(quant, sizeof(long int));
  set<long int> s;
  for (long int i = 0; i < quant; i++) {
    scanf("%ld", &nums[i]);
  }
  sort(nums, nums + quant);
  for (long int i = 0; i < quant; i++) {
    if (nums[i] % mul != 0 || s.count(nums[i] / mul) == 0) {
      s.insert(nums[i]);
    }
  }
  printf("%ld\n", s.size());
  free(nums);
  return 0;
}
