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.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class D2 {
    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int k = in.nextInt();

        int[] a = new int[n];

        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }

        out.println(solve(n, k, a));
        out.flush();
        out.close();
    }

    private static long solve(int n, int k, int[] a) {
        long ans = Long.MAX_VALUE;
        ArrayList<ArrayList<Integer>> al = new ArrayList<>();

        for (int i = 0; i <= 200000; i++) {
            al.add(new ArrayList<>());
        }

        for (int i = 0; i < n; i++) {
            int cur = 0;
            int x = a[i];
            while(x > 0) {
                al.get(x).add(cur++);
                x /= 2;
            }
        }

        for (int i = 0; i <= 200000; i++) {

            if(al.get(i).size() >= k) {
                Collections.sort(al.get(i));
                int temp = 0;
                for (int j = 0; j < k; j++) temp += al.get(i).get(j);
                ans = Math.min(ans, temp);
            }
        }
        return ans;
    }

    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;
        }
    }
}