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;
map<int, int> mm;
const int MAXNUM = 100005;
bool mark[MAXNUM];
int main() {
  int n, k;
  int nums[MAXNUM];
  int length[MAXNUM];
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &nums[i]);
  }
  sort(nums, nums + n);
  if (k == 1) {
    printf("%d\n", n);
    return 0;
  }
  for (int i = 0; i < n; i++) {
    int y = nums[i];
    length[i] = 1;
    if (y % k != 0) continue;
    int x = y / k;
    int p = lower_bound(nums, nums + n, x) - nums;
    if (nums[p] == x) {
      length[i] = length[p] + 1;
      length[p] = 0;
    }
  }
  int ans = 0;
  for (int i = 0; i < n; i++) {
    ans += (length[i] + 1) / 2;
  }
  printf("%d\n", ans);
  return 0;
}
