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.*;
import java.util.*;
 

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solution solver = new Solution();
		solver.solve(in, out);
        out.close();
    }
 
    static class Solution {
        public void solve(InputReader in, PrintWriter w) {

            int n=in.nextInt();
            int k=in.nextInt();
            int[] arr=new int[n];
            for(int i=0;i<n;i++) arr[i]=in.nextInt();
            ArrayList<Integer>[] a=new ArrayList[200005];
            for(int i=0;i<200005;i++) a[i]=new ArrayList<>();
            int div=0;
            for(int i=0;i<n;i++){
                div=0;
                while(arr[i]>0){
                    a[arr[i]].add(div);
                    arr[i]/=2;
                    div++;
                }
                a[0].add(div);
            }
            int min=Integer.MAX_VALUE;
            int sum=0;
            for(int i=0;i<200005;i++){
                if(a[i].size()>=k){
                    Collections.sort(a[i]);
                    sum=0;
                    for(int j=0;j<k;j++) sum+=a[i].get(j);
                    min=Math.min(min,sum);    
                }
            }
            w.println(min);
        
            
        }
    }

 
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
    }
}