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.util.*;
import java.io.*;

public class d {
    public static void main(String[] Args) 
        throws Exception
    {
        FS sc = new FS(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        HashSet<Integer> seen = new HashSet<Integer>();
        HashSet<Integer> occ = new HashSet<Integer>();
        
        Queue<Integer> q = new LinkedList<Integer>();
        
        for (int i = 0; i < n; i++)
        {
            int x = sc.nextInt();
            occ.add(x);
            q.add(x);
            q.add(0);
        }
        
        long total = 0;
        int placed = 0;
        int[] values = new int[m];
        while (placed < m) {
            int cur = q.poll();
            int dist = q.poll();
            if (occ.add(cur)) {
                total += dist;
                values[placed++] = cur;
            }
            if (seen.add(cur)) {
                q.add(cur+1);
                q.add(dist+1);
                q.add(cur-1);
                q.add(dist+1);
            }
        }
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        
        out.println(total);
        for (int i = 0; i < m; i++)
            out.print((values[i]) + " ");
        out.println();
        out.close();
    }
    
    public static class FS {
        BufferedReader br;
        StringTokenizer st;
        FS(InputStream in) 
            throws Exception
        {
            br = new BufferedReader(new InputStreamReader(in));
            st = new StringTokenizer(br.readLine());
        }
        String next()
            throws Exception
        {
            if (st.hasMoreTokens())
                return st.nextToken();
            st = new StringTokenizer(br.readLine());
            return next();
        }
        int nextInt()
            throws Exception
        {
            return Integer.parseInt(next());
        }
        long nextLong()
            throws Exception
        {
            return Long.parseLong(next());
        }
    }
}