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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ben King
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        D2EqualizingByDivisionHardVersion solver = new D2EqualizingByDivisionHardVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class D2EqualizingByDivisionHardVersion {
        int MAXN = 200010;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int N = in.nextInt();
            int M = in.nextInt();
            List<Integer> A = new ArrayList<>();
            for (int i = 0; i < N; i++) A.add(in.nextInt());
            int[] output = new int[2 * MAXN];

//        TreeNode root = new TreeNode(1, 0);
//        root.expand(counts, MAXN);

            Collections.sort(A);

            int best = Integer.MAX_VALUE;

            for (int a : A) {
                int x = a;
                int c = 0;
                while (x > 0) {
                    output[2 * x]++;
                    output[2 * x + 1] += c;
                    if (output[2 * x] >= M)
                        best = Math.min(best, output[2 * x + 1]);
                    x >>= 1;
                    ++c;
                }
            }

//        ArrayList<Integer> steps = new ArrayList<>();
//
//        for (int a : A) {
//            steps.clear();
//            int x = a;
//            while (x > 0) {
//                steps.add(x);
//                x >>= 1;
//            }
//            Collections.reverse(steps);
//            best = Math.min(best, root.insert(steps, M));
////            System.out.println(a + " " + best);
//        }
            out.println(best);

            out.flush();
        }

    }

    static class InputReader {
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
        private static final InputStream DEFAULT_STREAM = System.in;
        private int c;
        private byte[] buf;
        private int bufferSize;
        private int bufIndex;
        private int numBytesRead;
        private InputStream stream;
        private static final byte EOF = -1;
        private static final byte SPACE = 32;
        private static final byte DASH = 45;
        private char[] charBuffer;
        private static byte[] bytes = new byte[58];
        private static int[] ints = new int[58];
        private static char[] chars = new char[128];

        static {
            char ch = ' ';
            int value = 0;
            byte _byte = 0;
            for (int i = 48; i < 58; i++) bytes[i] = _byte++;
            for (int i = 48; i < 58; i++) ints[i] = value++;
            for (int i = 32; i < 128; i++) chars[i] = ch++;
        }

        public InputReader() {
            this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE);
        }

        public InputReader(int bufferSize) {
            this(DEFAULT_STREAM, bufferSize);
        }

        public InputReader(InputStream stream) {
            this(stream, DEFAULT_BUFFER_SIZE);
        }

        public InputReader(InputStream stream, int bufferSize) {
            if (stream == null || bufferSize <= 0)
                throw new IllegalArgumentException();
            buf = new byte[bufferSize];
            charBuffer = new char[128];
            this.bufferSize = bufferSize;
            this.stream = stream;
        }

        private int readJunk(int token) {

            if (numBytesRead == EOF) return EOF;

            // Seek to the first valid position index
            do {

                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] > token) return 0;
                    bufIndex++;
                }

                // reload buffer
                try {
                    numBytesRead = stream.read(buf);
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
                if (numBytesRead == EOF) return EOF;
                bufIndex = 0;

            } while (true);

        }

        public int nextInt() {
            try {
                if (readJunk(DASH - 1) == EOF) throw new IOException();
                int sgn = 1, res = 0;

                c = buf[bufIndex];
                if (c == DASH) {
                    sgn = -1;
                    bufIndex++;
                }

                do {

                    while (bufIndex < numBytesRead) {
                        if (buf[bufIndex] > SPACE) {
                            res = (res << 3) + (res << 1);
                            res += ints[buf[bufIndex++]];
                        }
                        else {
                            bufIndex++;
                            return res * sgn;
                        }
                    }

                    // Reload buffer
                    numBytesRead = stream.read(buf);
                    if (numBytesRead == EOF) return res * sgn;
                    bufIndex = 0;

                } while (true);
            }
            catch (IOException e) {
                e.printStackTrace();
                return -1;
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                outputStream)));
        }

        public OutputWriter(java.io.Writer outputStreamWriter) {
            writer = new PrintWriter(new BufferedWriter(outputStreamWriter));
        }

        public void flush() {
            writer.flush();
        }

        public void close() {
            writer.flush();
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}