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.sql.SQLOutput;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    static void bin(int n) {
        if (n > 1)
            bin(n/2);

        System.out.print(n % 2);
    }
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
    static class Pair<a , b>{
        a v1;
        b v2;
        Pair(a v1 , b v2){
            this.v1 = v1;
            this.v2 = v2;
        }
    }
    static class TaskA {
        public void solve(int testNumber, InputReader in, PrintWriter out){
            int n = in.nextInt();
            int m = in.nextInt();
            HashMap<Integer , Integer> map = new HashMap<>(n);
            ArrayList<Integer> arrayList = new ArrayList<>(m);
            Queue<Integer> queue = new LinkedList<>();
            for (int i = 0; i <n ; i++) {
                int index = in.nextInt();
                queue.add(index);
                map.put(index, 0);
            }
            long ans = 0;
            while (!queue.isEmpty()){
                if (m == 0) break;
                int s = queue.remove();
                if (map.get(s) > 0  ){
                    ans+=map.get(s);
                    arrayList.add(s);
                    m--;
                }
                if (!map.containsKey(s-1)){
                    map.put(s-1 ,map.get(s)+1);
                    queue.add(s-1);
                }
                if (!map.containsKey(s+1)){
                    map.put(s+1 , map.get(s)+1);
                    queue.add(s+1);
                }
            }
            System.out.println(ans)
            ;
            for (int i = 0; i <arrayList.size() ; i++) {
                System.out.print(arrayList.get(i)+" ");
            }
            System.out.println();



        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt(){return  Integer.parseInt(next());}
        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}