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.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.HashSet;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author xylenox
 */
public class d {
    static int MOD = 998244353;
    public static void main(String[] args) {
        FS in = new FS(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        int m = in.nextInt();
        ArrayDeque<Person> pq = new ArrayDeque<>();
        HashSet<Integer> poses = new HashSet<>();
        int[] arr = new int[n];
        for(int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            poses.add(arr[i]);
        }
        for(int i = 0; i < n; i++) {
            if(!poses.contains(arr[i]+1)) {
                poses.add(arr[i]+1);
                pq.add(new Person(arr[i]+1, 1, 1));
            }
            
            if(!poses.contains(arr[i]-1)) {
                poses.add(arr[i]-1);
                pq.add(new Person(arr[i]-1, -1, 1));
            }
        }
        long tot = 0;
        int[] res = new int[m];
        for(int i = 0; i < m; i++) {
            Person p = pq.poll();
            tot += p.dist;
            res[i] = p.ind;
            if(!poses.contains(p.ind+p.dir)) {
                poses.add(p.ind+p.dir);
                pq.add(new Person(p.ind+p.dir, p.dir, p.dist+1));
            }
        }
        out.println(tot);
        for(int i : res) out.print(i + " ");
        out.println();
        out.close();
    }
    
    static class Person {
        int ind, dir, dist;
        public Person(int I, int D, int DI) {
            ind = I;
            dir = D;
            dist = DI;
        }
    }

    static class FS {

        BufferedReader in;
        StringTokenizer token;

        public FS(InputStream st) {
            in = new BufferedReader(new InputStreamReader(st));
        }

        public String next() {
            if (token == null || !token.hasMoreElements()) {
                try {
                    token = new StringTokenizer(in.readLine());
                } catch (Exception e) {
                }
                return next();
            }
            return token.nextToken();
        }

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