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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, i, j, k, a, c;
  cin >> n >> k;
  vector<vector<int>> v(200015);
  for (i = 0; i < n; i++) {
    c = 0;
    cin >> a;
    while (a) {
      v[a].push_back(c);
      c++;
      a /= 2;
    }
    v[0].push_back(c);
  }
  int mn = INT_MAX;
  for (i = 0; i <= 200000; i++) {
    sort(v[i].begin(), v[i].end());
    for (j = 1; j < v[i].size(); j++) v[i][j] += v[i][j - 1];
  }
  for (i = 0; i <= 200000; i++)
    if (v[i].size() >= k) mn = min(mn, v[i][k - 1]);
  cout << mn << endl;
  return 0;
}