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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.util.HashSet;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class DChristmasTrees {
        public void solve(int testNumber, InputReader c, OutputWriter w) {
            int n = c.readInt(), m = c.readInt();
            HashSet<Integer> hs = new HashSet<>();
            for (int i = 0; i < n; i++) {
                hs.add(c.readInt());
            }
            TreeSet<dd> ts = new TreeSet<>();
            for (int kk : hs) {
//            System.out.println(kk);
                if (!hs.contains(kk + 1)) {
                    ts.add(new dd(1, kk + 1, true));
                }
                if (!hs.contains(kk - 1)) {
                    ts.add(new dd(1, kk - 1, false));
                }
            }

//        System.out.println(ts);
            long res = 0;
            HashSet<Integer> pp = new HashSet<>();
            while (pp.size() < m) {
//            System.out.println(ts);
                dd d1 = ts.pollFirst();
                int rt = d1.ind;
                if (pp.contains(rt)) {
                    continue;
                }
                pp.add(rt);
                res += d1.dist;
                if (d1.pos) {
                    if (!hs.contains(d1.ind + 1) && !pp.contains(d1.ind + 1)) {
                        ts.add(new dd(d1.dist + 1, d1.ind + 1, d1.pos));
                    }
                } else {
                    if (!hs.contains(d1.ind - 1) && !pp.contains(d1.ind - 1)) {
                        ts.add(new dd(d1.dist + 1, d1.ind - 1, d1.pos));
                    }
                }
            }
            w.printLine(res);
            for (int k : pp) {
                w.print(k + " ");
            }
            w.printLine();
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

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

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine() {
            writer.println();
        }

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

        public void printLine(long i) {
            writer.println(i);
        }

    }

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

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

        }

    }

    static class dd implements Comparable<dd> {
        int dist;
        int ind;
        boolean pos;

        public dd(int dist, int ind, boolean pos) {
            this.dist = dist;
            this.ind = ind;
            this.pos = pos;
        }

        public String toString() {
            return "dd{" +
                    "dist=" + dist +
                    ", ind=" + ind +
                    ", pos=" + pos +
                    '}';
        }

        public int compareTo(dd o) {
            if (this.dist == o.dist) {
                return this.ind - o.ind;
            }
            return this.dist - o.dist;
        }

    }
}

