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 a{
   
    public static void main(String [] args)throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String [] data=br.readLine().trim().split(" ");
        int n=Integer.parseInt(data[0]);
        int m=Integer.parseInt(data[1]);
        data=br.readLine().trim().split(" ");
        int [] a=new int[n];
        Queue<Integer> q=new LinkedList<>();
        TreeSet<Integer> tset=new TreeSet<>();
        Map<Integer,Integer> map=new HashMap<>();

        for(int i=0;i<n;i++){
            a[i]=Integer.parseInt(data[i]);
            q.add(a[i]);
            map.put(a[i],1);
            tset.add(a[i]);
        }

        int cnt=0;
        List<Integer> list=new ArrayList<>();
        while(!q.isEmpty() && cnt<m){
            int u=q.poll();
            if(!map.containsKey(u+1) && cnt<m){
                q.add(u+1);
                list.add(u+1);
                map.put(u+1,1);
                cnt++;
            }
            if(!map.containsKey(u-1) && cnt<m){
                q.add(u-1);
                list.add(u-1);
                map.put(u-1,1);
                cnt++;
            }
        }
        long sum=0;
        for(int i : list){
            Integer lower=tset.lower(i);
            Integer higher=tset.higher(i);
            if(lower!=null && higher !=null)
                sum+=Math.min(Math.abs(i-lower),Math.abs(i-higher));
            else if(lower!=null)
                sum+=Math.abs(i-lower);
            else  
               sum+=Math.abs(i-higher);

        }
        System.out.println(sum);
        StringBuilder ss=new StringBuilder("");
        for(int i : list){
            ss.append(i+" ");
        }

        System.out.println(ss.toString());

    }
}