There are n Christmas trees on an infinite number line. The i-th tree grows at the position x_i. All x_i are guaranteed to be distinct.

Each integer point can be either occupied by the Christmas tree, by the human or not occupied at all. Non-integer points cannot be occupied by anything.

There are m people who want to celebrate Christmas. Let y_1, y_2, ..., y_m be the positions of people (note that all values x_1, x_2, ..., x_n, y_1, y_2, ..., y_m should be distinct and all y_j should be integer). You want to find such an arrangement of people that the value ∑_{j=1}^{m}min_{i=1}^{n}|x_i - y_j| is the minimum possible (in other words, the sum of distances to the nearest Christmas tree for all people should be minimized).

In other words, let d_j be the distance from the j-th human to the nearest Christmas tree (d_j = min_{i=1}^{n} |y_j - x_i|). Then you need to choose such positions y_1, y_2, ..., y_m that ∑_{j=1}^{m} d_j is the minimum possible.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the number of Christmas trees and the number of people.

The second line of the input contains n integers x_1, x_2, ..., x_n (-10^9 ≤ x_i ≤ 10^9), where x_i is the position of the i-th Christmas tree. It is guaranteed that all x_i are distinct.

Output

In the first line print one integer res — the minimum possible value of ∑_{j=1}^{m}min_{i=1}^{n}|x_i - y_j| (in other words, the sum of distances to the nearest Christmas tree for all people).

In the second line print m integers y_1, y_2, ..., y_m (-2 ⋅ 10^9 ≤ y_j ≤ 2 ⋅ 10^9), where y_j is the position of the j-th human. All y_j should be distinct and all values x_1, x_2, ..., x_n, y_1, y_2, ..., y_m should be distinct.

If there are multiple answers, print any of them.

Examples

Input


2 6
1 5


Output


8
-1 2 6 4 0 3 


Input


3 5
0 3 1


Output


7
5 -2 4 -1 2 
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Collection;
import java.util.Set;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.ArrayDeque;
import java.util.Comparator;
import java.io.InputStream;

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

    static class DChristmasTrees {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            Queue<Integer> pos = new ArrayDeque<>(n);
            Set<Integer> used = new HashSet<>();
            Map<Integer, Integer> distance = new HashMap<>();
            Map<Integer, Integer> res = new HashMap<>();
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt();
                used.add(x);
                distance.put(x, 0);
                pos.add(x);
            }
            int[] dx = {-1, 1};
            while (!pos.isEmpty() && res.keySet().size() < m) {
                int cur = pos.poll();
                for (int x : dx) {
                    int p = cur + x;
                    if (used.contains(p)) continue;
                    used.add(p);
                    distance.put(p, distance.get(cur) + 1);
                    res.put(p, distance.get(cur) + 1);
                    pos.add(p);
                }
            }
            long ans = 0;
            List<Integer> print = new ArrayList<>(m);
            ArrayList<Map.Entry<Integer, Integer>> entries = new ArrayList<>(res.entrySet());
            entries.sort(Comparator.comparingInt(Map.Entry::getValue));
            for (int i = 0; i < m; ++i) {
                ans += entries.get(i).getValue();
            }
            out.println(ans);
            for (int i = 0; i < m; ++i) {
                if (i > 0) out.print(" ");
                out.print(entries.get(i).getKey());
            }
            out.println();
        }

    }

    static class InputReader {
        private InputStream stream;
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
        private static final int EOF = -1;
        private byte[] buf = new byte[DEFAULT_BUFFER_SIZE];
        private int curChar;
        private int numChars;

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

        public int read() {
            if (this.numChars == EOF) {
                throw new UnknownError();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException ex) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return EOF;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == EOF;
        }

    }
}

