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.util.Arrays;
import java.util.PriorityQueue;
import java.io.BufferedWriter;
import java.util.HashMap;
import java.util.AbstractCollection;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;

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

    static class D2EqualizingByDivisionHardVersion {
        int N;
        int K;

        public void solve(int testNumber, FastReader in, FastWriter out) {
            int i, j, k;

            N = in.nextInt();
            K = in.nextInt();
            Long[] A = new Long[N];
            for (i = 0; i < N; ++i) A[i] = in.nextLong();
            Arrays.sort(A);

            HashMap<Long, PriorityQueue<Integer>> map = new HashMap<>();
            for (long itr : A) {
                for (i = 0; ; ++i) {
                    map.put(itr, add(map.get(itr), i));
                    if (itr <= 0) break;
                    itr >>= 1;
                }
            }

            long ans = Long.MAX_VALUE >> 2;
            for (PriorityQueue<Integer> pq : map.values())
                if (pq.size() == K) {
                    long temp = 0;
                    while (!pq.isEmpty()) temp += pq.poll();
                    ans = Math.min(ans, temp);
                }
            out.println(ans);

            out.flush();
        }

        PriorityQueue<Integer> add(PriorityQueue<Integer> pq, int val) {
            if (pq == null) pq = new PriorityQueue<>(Comparator.reverseOrder());
            pq.add(val);
            while (pq.size() > K) pq.poll();
            return pq;
        }

    }

    static class FastReader {
        static private byte[] buf = new byte[2048];
        static private int index;
        static private int total;
        static private InputStream in;

        public FastReader(InputStream is) {
            try {
                in = is;
            } catch (Exception e) {
            }
        }

        private int scan() {
            try {
                if (index >= total) {
                    index = 0;
                    total = in.read(buf);
                    if (total <= 0)
                        return -1;
                }
                return buf[index++];
            } catch (Exception e) {
                return 7 / 0;
            }
        }

        public int nextInt() {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+')
                c = scan();
            for (; c >= '0' && c <= '9'; c = scan())
                val = (val << 3) + (val << 1) + (c & 15);
            return neg ? -val : val;
        }

        public long nextLong() {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+')
                c = scan();
            for (; c >= '0' && c <= '9'; c = scan())
                val = (val << 3) + (val << 1) + (c & 15);
            return neg ? -val : val;
        }

    }

    static class FastWriter {
        static private BufferedWriter bw;

        public FastWriter(OutputStream os) {
            bw = new BufferedWriter(new OutputStreamWriter(os));
        }

        public FastWriter(Writer w) {
            bw = new BufferedWriter(w);
        }

        public void print(Object a) {
            try {
                bw.write(a.toString());
            } catch (Exception e) {
            }
        }

        public void println(Object a) {
            print(a);
            print("\n");
        }

        public void flush() {
            try {
                bw.flush();
            } catch (Exception e) {
            }
        }

        public void close() {
            try {
                bw.close();
            } catch (Exception e) {
            }
        }

    }
}