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.function.IntConsumer;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Deque;
import java.util.TreeSet;
import java.util.ArrayList;
import java.util.List;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD(in, out);
        try {
            solver.solve();
        } catch (ExitException ignored) {
        }
        out.close();
    }

    static class TaskD {
        FastScanner sc;
        PrintWriter out;

        public TaskD(FastScanner sc, PrintWriter out) {
            this.sc = sc;
            this.out = out;
        }

        public void solve() {
            times(1, this::solve);
        }

        public void solve(int time) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            TreeSet<Integer> points = new TreeSet<>();
            Deque<TaskD.Point> from = new ArrayDeque<>(n * 2);
            List<Integer> ans = new ArrayList<>();

            for (int i = 0; i < n; i++) {
                int tree = sc.nextInt();
                points.add(tree);
                from.add(new TaskD.Point(tree, 1, -1));
                from.add(new TaskD.Point(tree, 1, +1));
            }

            long ians = 0;
            while (ans.size() < m) {
                TaskD.Point point = from.pollFirst();
                int next = point.x + point.dir;
                if (points.add(next)) {
                    ans.add(next);
                    ians += point.level;
                    from.add(new TaskD.Point(next, point.level + 1, point.dir));
                }
            }

            writeln(ians);
            for (int i = 0; i < m; i++) {
                write(ans.get(i) + " ");
            }
            answer("");
        }

        private void write(Object obj) {
            out.print(obj);
        }

        private void writeln(Object obj) {
            out.println(obj);
        }

        private void answer(Object ans) {
            out.println(ans);
            throw new ExitException();
        }

        private void times(int n, IntConsumer consumer) {
            for (int i = 0; i < n; i++) {
                try {
                    consumer.accept(i);
                } catch (ExitException ignored) {
                }
            }
        }

        static class Point {
            int x;
            int level;
            int dir;

            public Point(int x, int level, int dir) {
                this.x = x;
                this.level = level;
                this.dir = dir;
            }

        }

    }

    static class ExitException extends RuntimeException {
    }

    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        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++];
        }

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

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

    }
}

