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

public class Main {

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

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

        public char nextChar() {
            return next().charAt(0);
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }

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

        public int[] nextIntArray(int n) {
            int[] intArray = new int[n];
            for (int i = 0; i < n; i++) {
                intArray[i] = nextInt();
            }
            return intArray;
        }
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        int q = 1;
        for (int i = 0; i < q; i++) {
            solver.solve(i + 1, in, out);
        }
        out.close();
    }

    static class Task {

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int[] s = new int[n];
            int[] s1 = new int[200005];
            int[] s2 = new int[200005];
            int max = Integer.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                s[i] = in.nextInt();
                if (s[i] > max) {
                    max = s[i];
                }
            }
            Arrays.sort(s);
            for (int i = 0; i < n; i++) {
                int count = 0;
                while (s[i] != 0) {
                    s1[s[i]]++;
                    if (s1[s[i]] <= m) {
                        s2[s[i]] += count;
                    }
                    count++;
                    s[i] /= 2;
                }
                s1[0]++;
                if (s1[0] <= m) {
                    s2[0] += count;
                }
            }
            int mi = Integer.MAX_VALUE;
            for (int i = 0; i <= max; i++) {
                if (s1[i] >= m) {
                    mi = Math.min(mi, s2[i]);
                }
            }
            out.println(mi);
        }
    }
}