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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
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);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            ArrayList<Long> a = new ArrayList<>();
            for (int i = 0; i < n; i++) a.add(in.nextLong());
            Collections.sort(a);
            ArrayList<long[]> cnt = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (cnt.size() == 0) {
                    cnt.add(new long[]{a.get(i), 1});
                    continue;
                }
                if (cnt.get(cnt.size() - 1)[0] == a.get(i)) cnt.get(cnt.size() - 1)[1]++;
                else cnt.add(new long[]{a.get(i), 1});
            }
            int nn = cnt.size();
            long pre[][] = new long[nn + 1][2];
            long post[][] = new long[nn + 1][2];
            for (int i = 1; i <= nn; i++) {
                pre[i][0] += cnt.get(i - 1)[0] * cnt.get(i - 1)[1];
                pre[i][0] += pre[i - 1][0];
                pre[i][1] += cnt.get(i - 1)[1];
                pre[i][1] += pre[i - 1][1];
            }
            for (int i = nn - 1; i >= 0; i--) {
                post[i][0] += cnt.get(i)[0] * cnt.get(i)[1];
                post[i][0] += post[i + 1][0];
                post[i][1] += cnt.get(i)[1];
                post[i][1] += post[i + 1][1];
            }
            long ans = Long.MAX_VALUE;
//        for(int i=0;i<nn;i++){
//            out.print(cnt.get(i)[0]+ "+" +cnt.get(i)[1] + " ");
//        }
//        out.println();
//        for(int i=0;i<=nn;i++){
//            out.print(pre[i][0]+ "+" +pre[i][1] + " ");
//        }
//        out.println();
//        for(int i=0;i<=nn;i++){
//            out.print(post[i][0]+ "+" +post[i][1] + " ");
//        }
//        out.println();
            for (int i = 0; i < nn; i++) {
                long reqd = Math.max(0, k - cnt.get(i)[1]);
                if (reqd == 0) {
                    out.println(0);
                    return;
                }
                long leftc = pre[i][1];
                long leftsum = (leftc * (cnt.get(i)[0] - 1)) - pre[i][0];
                long rightc = post[i + 1][1];
                long rightsum = -(rightc * (cnt.get(i)[0] + 1)) + post[i + 1][0];
                if (leftc >= reqd) {
                    ans = Math.min(leftsum + reqd, ans);
                }
                if (rightc >= reqd) {
                    ans = Math.min(rightsum + reqd, ans);
                }
                ans = Math.min(leftsum + rightsum + reqd, ans);
//            out.println(ans + " " + rightsum + " " + leftsum);
            }
            out.println(ans);
        }

    }

    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());
        }

    }
}