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 A{
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
        
        int nc=sc.nextInt();
        int nh=sc.nextInt();
        
        Queue<Integer> q=new LinkedList<>();
        //HashSet<Integer> ans=new HashSet<>();
        HashMap<Integer,Long> hs=new HashMap<>();
        int[] ans=new int[nh];
        
        int n=0;
        for(int i=0;i<nc;i++)
         {
             int xx=sc.nextInt();
             
             q.add(xx);
             hs.put(xx,(long)0); 
             
         }
         
         long dis=0;
         while(!q.isEmpty())
          {
              
              if(n==nh)
                break;
              int nn=q.poll();
              
             if(hs.get(nn)!=0)
                {
                    dis+=hs.get(nn);
                    ans[n]=nn;
                    n++;
                }
              // System.out.println(dis);
              if(!hs.containsKey(nn+1))
               {
                   q.add(nn+1);
                   hs.put(nn+1,hs.get(nn)+1);
               }
               
                if(!hs.containsKey(nn-1))
               {
                   q.add(nn-1);
                   hs.put(nn-1,hs.get(nn)+1);
               }
              
          }
          
          System.out.println(dis);
          
          for(int i: ans)
            System.out.print(i+" ");
        
        
    }
}