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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.StringTokenizer;

public class EqualizingByDivision {
    public static void main(String[] args) {
        FastReader input=new FastReader();
        int n,k;
        n=input.nextInt();
        k=input.nextInt();
        int a[]=new int[n];
        int max=Integer.MIN_VALUE;
        for(int i=0;i<n;i++)
        {
            a[i]=input.nextInt();
            max=Math.max(max,a[i]);
        }
        ArrayList<ArrayList<Integer>> list=new ArrayList<>();
        for(int i=0;i<=max;i++)
        {
            ArrayList<Integer> l=new ArrayList<>();
            for(int j=0;j<n;j++)
            {
                int nu=a[j];
                int c=0;
                int flag=0;
                while(nu!=0)
                {
                    if(nu==i)
                    {
                        flag=1;
                        break;
                    }
                    c++;
                    nu=nu/2;
                }
                if(flag==1)
                {
                    l.add(c);
                }
                else
                {
                    if(i==0)
                    {
                        l.add(c);
                    }
                }
            }
            list.add(l);
        }
        int min=Integer.MAX_VALUE;
        for(int i=0;i<list.size();i++)
        {
            if(list.get(i).size()>=k)
            {
                Collections.sort(list.get(i));
                int sum=0;
                for(int j=0;j<k;j++)
                {
                    sum+=list.get(i).get(j);
                }
                min=Math.min(min,sum);
            }
        }
        System.out.println(min);
    }
    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;
        }
    }
}