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.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.HashMap;
import java.util.ArrayList;
import java.util.Collections;

public class Main
{
	public static void main(String[] args)
	{
		FastReader fr =new FastReader();

		PrintWriter op =new PrintWriter(System.out);

		int n =fr.nextInt() ,k =fr.nextInt() ,i ,j ,a ;	HashMap<Integer , Integer> ctr ;
		ctr =new HashMap<Integer , Integer>() ;	
		HashMap<Integer , ArrayList<Integer>> stp =new HashMap<Integer , ArrayList<Integer>>() ;

		for (i =0 ; i<n ; ++i) {
			a =fr.nextInt() ;	j =0 ;

			while (a >= 0) {
				if (ctr.containsKey(a))	ctr.put(a , ctr.get(a)+1) ;
				else {
					ctr.put(a , 1) ;	stp.put(a , new ArrayList<Integer>()) ;
				}
				stp.get(a).add(j) ;	
				if (a > 0)	a /= 2 ;	else 	a =-1 ;	++j ;

			}			
		}//System.out.println(stp) ;System.out.println(ctr) ;
		int ans =Integer.MAX_VALUE ;
		for (int key : ctr.keySet()) {
			if (ctr.get(key) >=k ) {
				ArrayList<Integer> dm =stp.get(key) ;	Collections.sort(dm) ;
				//System.out.println(dm) ;
				j =0 ;
				if (dm.size() >=k) {
					for (i =0 ; i<k ; ++i) {
						j += dm.get(i) ;
					}
					ans =Math.min(j , ans) ;
				}
			}
		}
		op.println(ans) ;
		op.flush();	op.close();
	}

	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();
		}

		String nextLine() {
			String str ="";

			try
			{
				str =br.readLine();
			}
			catch(IOException e)
			{
				e.printStackTrace();
			}

			return str;
		}

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

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