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.*;
import java.util.*;


public class Sol {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = sc.nextInt();
        HashSet<Integer> visited = new HashSet<>();
        ArrayList<Integer> sol = new ArrayList<>();
        ArrayDeque<Pair> q = new ArrayDeque<>();
        for (int i = 0; i < n; i++) {
            int e = sc.nextInt();
            q.add(new Pair(e, e));
            visited.add(e);
        }
        long dist = 0;
        while (m > 0) {
            Pair poll = q.poll();
            if (!visited.contains(poll.a + 1)) {
                q.add(new Pair(poll.a + 1, poll.b));
                dist += Math.abs(poll.a + 1 - poll.b);
                m--;
                sol.add(poll.a + 1);
                visited.add(poll.a + 1);
            }
            if (m <= 0) {
                break;
            }
            if (!visited.contains(poll.a - 1)) {
                q.add(new Pair(poll.a - 1, poll.b));
                m--;
                dist += Math.abs(poll.a - 1 - poll.b);
                sol.add(poll.a - 1);
                visited.add(poll.a - 1);
            }
        }
        out.println(dist);

        for (Integer integer : sol) {
            out.print(integer + " ");
        }
        out.flush();
        out.close();
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;

        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Pair o) {
            return this.a - o.a;
        }
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream System) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(System));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() {
            for (long i = 0; i < 3e9; i++)
                ;
        }
    }
}
