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 JAVA):

Solution:

import java.util.*;

public class Result {

    private static final Scanner scanner = new Scanner(System.in);

    public static void main(String[] args){
      int n = scanner.nextInt();
      int k = scanner.nextInt();
      int x,curr,ans=(int)1e9,sum=0;
      int[] a = new int[n];
      for (int i=0;i<n;i++)
          a[i]=scanner.nextInt();
      ArrayList<Integer>[] list = new ArrayList[200005];
        for (int i = 0; i < 200005; i++) {
            list[i] = new ArrayList<>();
        }

        for (int i=0;i<n;i++){
          x=a[i];
          curr=0;
          while (x>0){
              list[x].add(curr);
              x/=2;
              curr++;
          }
      }
      for (int i=0;i<200005;i++){
          sum=0;
          Collections.sort(list[i]);
          if (list[i].size()<k)
              continue;
          for (int j=0;j<k;j++)
              sum+=list[i].get(j);
          ans=Math.min(ans,sum);
      }
        System.out.println(ans);
        scanner.close();
    }
}