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.lang.reflect.Array;
import java.util.*;

public class Q1 {


    public static void main(String[] args) {

        InputReader in = new InputReader();

        int N = in.nextInt(),K=in.nextInt();
        int arr[] = new int[N];
        ArrayList<Integer> list[]=new ArrayList[(int)2*100009];

      //  System.out.println(list.length);
        for(int i=0;i<list.length;i++) {
            list[i] = new ArrayList<>();
        }

        for (int i = 0; i < N; i++) {
            arr[i] = in.nextInt();
            int c=0;
            while(true) {
                list[arr[i]].add(c);
                if (arr[i] == 0)
                    break;
                arr[i] = arr[i] / 2;
                c++;
            }
        }

        int ans=Integer.MAX_VALUE;
        for(int i=0;i<list.length;i++){
            if(list[i].size()<K)
                continue;
            int c=0;
            Collections.sort(list[i]);
            for(int j=0;j<list[i].size() && j<K;j++)
                c+=list[i].get(j);

            if(c<ans)
                ans=c;

        }

        System.out.println(ans);


    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public int[] shuffle(int[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                arr[i] = arr[i] ^ arr[j];
                arr[j] = arr[i] ^ arr[j];
                arr[i] = arr[i] ^ arr[j];
            }
            return arr;
        }

        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(System.in), 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 char nextChar() {
            return next().charAt(0);
        }

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

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

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


    }

}