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.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class AE4 {
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int n=scan.nextInt();
        int k=scan.nextInt();
        int[] arr=new int[n];
        int min=Integer.MIN_VALUE;
        for (int i = 0; i <n ; i++) {
            arr[i]=scan.nextInt();
            min=Math.max(min,arr[i]);
        }
        Map<Integer,PriorityQueue<Integer>> map=new HashMap<>();
        for(int i=0;i<n;i++){
            int t=0;
            while(arr[i]>0){
                map.putIfAbsent(arr[i],new PriorityQueue<>());
                map.get(arr[i]).add(t);
                t++;
                arr[i]/=2;
            }
            map.putIfAbsent(0,new PriorityQueue<>());
            map.get(0).add(t);
        }
        int ans=Integer.MAX_VALUE;
        for(Integer i:map.keySet()){
            int local=0;
            PriorityQueue<Integer> cur=map.get(i);
            if(cur.size()>=k){
                for(int j=0;j<k;j++){
                    local+=cur.remove();
                }
                ans=Math.min(local,ans);
            }
        }
        System.out.println(ans);
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

}