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.util.TreeMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class FMakeKEqual {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            int n = s.nextInt();
            int k = s.nextInt();

            int arr[] = s.nextIntArray(n);
            TreeMap<Integer, Integer> map = new TreeMap();
            long sum = 0;
            for (int i = 0; i < n; i++) {
                map.putIfAbsent(arr[i], 0);
                map.put(arr[i], map.get(arr[i]) + 1);
                sum += arr[i];
            }


            Pair left[] = new Pair[map.size()];
            Pair right[] = new Pair[map.size()];
            int index = 0;
            for (Map.Entry<Integer, Integer> et : map.entrySet()) {
                if (et.getValue() >= k) {
                    out.println("0");
                    return;
                }
                if (index > 0) {
                    left[index] = new Pair(et.getKey(), et.getValue() + left[index - 1].countSum, 1L * et.getKey() * et.getValue() + left[index - 1].sum);
                    right[index] = new Pair(et.getKey(), n - left[index - 1].countSum, sum - left[index - 1].sum);
                } else {
                    left[index] = new Pair(et.getKey(), et.getValue(), 1L * et.getKey() * et.getValue());
                    right[index] = new Pair(et.getKey(), n, sum);
                }
                index++;
            }
            int sz = map.size();
            long ans = Long.MAX_VALUE;
            for (int i = 0; i < sz; i++) {
                long ll = 0;
                int vCrl = 0;
                if (i > 0) {
                    ll = 1L * left[i - 1].countSum * (left[i].val - 1) - left[i - 1].sum;
                    vCrl = left[i - 1].countSum;
                }
                long rr = 0;
                int vCrr = 0;
                if (i < sz - 1) {
                    rr = right[i + 1].sum - 1L * right[i + 1].countSum * (right[i].val + 1);
                    vCrr = right[i + 1].countSum;
                }

                if (vCrl >= k - map.get(left[i].val)) {
                    ans = Math.min(ans, (ll + k - map.get(left[i].val)));
                }
                if (vCrr >= k - map.get(right[i].val)) {
                    ans = Math.min(ans, (rr + k - map.get(right[i].val)));
                }
                ans = Math.min(ans, rr + ll + k - map.get(right[i].val));
            }
            out.println(ans);
        }

        class Pair {
            int val;
            int countSum;
            long sum;

            Pair(int val, int countSum, long sum) {
                this.val = val;
                this.countSum = countSum;
                this.sum = sum;
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}