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.Scanner;
import java.util.Arrays;
import java.util.ArrayList;
public class Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int k = s.nextInt();
        int arr[] = new int[n];
        int max = -1;
        for(int i = 0; i < n; i++){
            arr[i] = s.nextInt();
            max = Math.max(max,arr[i]);
        }
        Arrays.sort(arr);
        int ans = Integer.MAX_VALUE;
        for(int i = max; i >= 0; i--){
            ArrayList<Integer> list = new ArrayList<>();
            for(int j = n - 1;j >= 0; j--){
                int opt = 0,safe = arr[j];
                while(safe > i){
                    safe = safe/2;
                    opt++;
                }
                if(safe == i){
                    list.add(opt);
                }
            }
            if(list.size() >= k){
                int sum = 0;
                int times = 0;
                for(int start = list.size() - 1; start >= 0 && times < k; start--){
                    sum += list.get(start);
                    times++;
                }
                ans = Math.min(ans,sum);
            }

        }
        System.out.println(ans);
        
    }
   

    
}