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.*;
public class Main
{
    public static class Node implements Comparable<Node> 
    {
        int v;
        int tmp;
        int c;
        Node(int x,int y)
        {
            v=x;
            tmp=y;
            c=y;
        }
        public int compareTo(Node b)
        {
            return b.v-v;
        }
    }
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int[] arr=new int[n];
		TreeSet<Integer> set=new TreeSet();
		for(int i=0;i<n;i++)
		{
		    arr[i]=sc.nextInt();
		    set.add(arr[i]);
		}
		TreeSet<Node>[]brr=new TreeSet[2];
		brr[0]=new TreeSet();
		brr[1]=new TreeSet();
		for(int i=0;i<n;i++)
		   {brr[0].add(new Node(arr[i],1));brr[1].add(new Node(arr[i],-1));}
		StringBuilder str=new StringBuilder();
		int t=0,i=0;
		long ans=0;
		while(i<m)
		{
		       Iterator itr=brr[t].iterator();
		       ArrayList<Node> list=new ArrayList();
		       while(itr.hasNext())
		       {
		           Node x=(Node)itr.next();
		           if(set.contains(x.v+x.tmp))
		           {
		               list.add(x);
		           }
		           else {
		           str.append(x.v+x.tmp);
		           ans+=Math.abs(Long.valueOf(x.tmp));
		           str.append(" ");
		           set.add(x.v+x.tmp);
		           x.tmp+=x.c;i++;
		           if(i==m)
		           break;
		           }
		       }
		       for(Node x:list)
		       brr[t].remove(x);
		       t^=1;
		}
		System.out.println(ans+"\n"+str);
	}
}
