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.util.*;

public class Task {

    public static void main(String[] args) throws Exception {

        new Task().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    Task() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            //in = new Reader("input.txt");
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws Exception {

        //int t = in.nextInt();
        int t = 1;
        while (t > 0) {
            solve();
            t--;
        }

        out.flush();
        out.close();
    }


    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;

    ArrayList<Integer>[] g;

    void solve() throws IOException {

        int n = in.nextInt();
        int k = in.nextInt();
        int[] a = new int[n];
        TreeMap<Integer, Integer> count = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            int c = count.getOrDefault(a[i], 0);
            count.put(a[i], c + 1);
        }
        HashMap<Integer, Long> dec = new HashMap<>();
        HashMap<Integer, Long> inc = new HashMap<>();
        HashMap<Integer, Integer> next = new HashMap<>();

        int prev = -1;
        int cnt = 0;
        ArrayDeque<Integer> st = new ArrayDeque<>();
        for (int x : count.keySet()) {
            st.push(x);
            if (prev == -1) {
                inc.put(x, 0L);
            } else {
                long diff = x - prev;
                inc.put(x, inc.get(prev) + cnt * diff);
            }
            prev = x;
            cnt += count.get(x);
        }

        prev = -1;
        cnt = 0;
        while (!st.isEmpty()) {
            int x = st.pop();
            next.put(x, prev);
            if (prev == -1) {
                dec.put(x, 0L);
            } else {
                long diff = prev - x;
                dec.put(x, dec.get(prev) + cnt * diff);
            }
            prev = x;
            cnt += count.get(x);
        }

        long ans = Long.MAX_VALUE;

        prev = -1;
        int cnt1 = 0;
        int cnt2 = n;
        for (int x : count.keySet()) {
            int nxt = next.get(x);
            int curCount = count.get(x);
            long need = Math.max(k - curCount, 0);
            cnt2 -= curCount;

            if (need == 0) {
                ans = 0;
                break;
            }

            if (prev != -1) {
                long s = inc.get(x);
                if (cnt1 >= need) {
                    ans = Math.min(s - (cnt1 - need), ans);
                }
            }

            if (nxt != -1) {
                long s = dec.get(x);
                 if (cnt2 >= need) {
                     ans = Math.min(s - (cnt2 - need), ans);
                 }
            }

            if (nxt != -1 && prev != -1) {
                long s = inc.get(x) + dec.get(x);
                ans = Math.min(s - (cnt1 + cnt2 - need), ans);
            }
            prev = x;
            cnt1 += curCount;
        }

        out.println(ans);
    }


    class Pair implements Comparable<Pair> {

        int a;
        int b;

        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {
            if (a != p.a)
                return Integer.compare(a, p.a);
            else
                return Integer.compare(b, p.b);
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }


    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

    static class InputReader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

}