Problem: You are given the array a consisting of n elements and the integer k ≤ n.

You want to obtain at least k equal elements in the array a. In one move, you can make one of the following two operations:

  * Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of a is mn then you choose such index i that a_i = mn and set a_i := a_i + 1); 
  * take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of a is mx then you choose such index i that a_i = mx and set a_i := a_i - 1). 



Your task is to calculate the minimum number of moves required to obtain at least k equal elements in the array.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and the required number of equal elements.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the minimum number of moves required to obtain at least k equal elements in the array.

Examples

Input


6 5
1 2 2 4 2 3


Output


3


Input


7 5
3 3 2 1 1 1 3


Output


4

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k, i, t;
  cin >> n >> k;
  vector<int> a(n);
  set<int> s;
  for (i = 0; i < n; i++) {
    cin >> t;
    a[i] = t;
    while (t) {
      s.insert(t);
      t /= 2;
    }
  }
  int ans = INT_MAX;
  for (auto x : s) {
    vector<int> cur;
    for (i = 0; i < n; i++) {
      int cnt = 0;
      t = a[i];
      while (t > x) {
        t /= 2;
        cnt++;
      }
      if (t == x) cur.push_back(cnt);
    }
    if ((int)(cur).size() < k) continue;
    sort(cur.begin(), cur.end());
    ans = min(ans, accumulate(cur.begin(), cur.begin() + k, 0));
  }
  cout << ans << endl;
}