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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;


/* Name of the class has to be "Main" only if the class is public. */
public class p6
{
         static class Input {
        private StringTokenizer tokenizer = null;
        private BufferedReader reader;
 
        public Input(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }
 
        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(nextLine());
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public int[] nextIntArray(int n, int add) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt() + add;
            }
            return result;
        }
 
        public long[] nextLongArray(int n, long add) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong() + add;
            }
            return result;
        }
 
        public int[] nextIntArray(int n) {
            return nextIntArray(n, 0);
        }
 
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		Input s=new Input(System.in);
		int t=1;
		PrintWriter out=new PrintWriter(System.out);
		
		while(t-->0)
		{
            int n=s.nextInt();
            int k=s.nextInt();
            TreeMap<Long,Long> tr=new TreeMap<>();
            for(int i=0;i<n;i++)
            {
                long te=s.nextLong();
                tr.put(te,tr.getOrDefault(te,(long)0)+1);
            }
            n=tr.size();
            long lsum[]=new long[n];
            long rsum[]=new long[n];
            long lcnt[]=new long[n];
            long rcnt[]=new long[n];
            long ar[]=new long[n];
            long fr[]=new long[n];
            int in=0;
            for(Long ke:tr.keySet())
            {    ar[in]=ke;
                 fr[in++]=tr.get(ke);
            }
             
            lcnt[0]=fr[0];
            lsum[0]=fr[0]*ar[0];
            rcnt[n-1]=fr[n-1];
            rsum[n-1]=ar[n-1]*fr[n-1];
            
            for(int i=1;i<n;i++)
            {lcnt[i]=lcnt[i-1]+fr[i];
             lsum[i]=lsum[i-1]+fr[i]*ar[i];
            }

            for(int i=n-2;i>=0;i--)
            {
                rcnt[i]=rcnt[i+1]+fr[i];
                rsum[i]=rsum[i+1]+fr[i]*ar[i];
            }

            long ans=Long.MAX_VALUE;
            for(int i=0;i<n;i++)
            {
                long need=Math.max((long)k-fr[i],(long)0);
                long needl=0;
                long op=0;
                
                if(need==0)
                {ans=0;
                    break;}
                if(i>0)
                {needl=Math.min(lcnt[i-1],need);
                op+=lcnt[i-1]*(ar[i]-1)-lsum[i-1];
                 op+=needl;
                }
                long needr=0;
                if(i<n-1){
                 needr=Math.min(rcnt[i+1],need-needl);
                 if(needr>0)
                 op+=rsum[i+1]-(ar[i]+1)*rcnt[i+1];
                 op+=needr;   
                }
                
                ans=Math.min(ans,op);
            }

            for(int i=0;i<n;i++)
            {
                long need=Math.max((long)k-fr[i],0);
                if(need==0)
                {ans=0;
                    break;}
                
                long op=0;
                
                long needr=0;
                if(i<n-1){
                needr=Math.min(rcnt[i+1],need);
                //out.println(rsum[i+1]+" "+(ar[i]+1)+" "+rcnt[i+1]);
                 op+=rsum[i+1]-(ar[i]+1)*rcnt[i+1];
                 op+=needr; 
                }
                
                long needl=0;
                if(i>0)
                {needl=Math.min(lcnt[i-1],need-needr);
                 if(needl>0)
                 op+=lcnt[i-1]*(ar[i]-1)-lsum[i-1];
                 op+=needl;
                }
                //out.println("needl"+needl+"needr"+needr);
                //out.println(op+" "+ar[i]);
                ans=Math.min(ans,op);
            }
            out.println(ans);
        }
        out.flush();
	}
}