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 Main
{
	static Scanner input = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out, true);

	public static void main(String[] args)
	{
		Integer m, n ;
		n = input.nextInt();
		m = input.nextInt();

		long s_distance = 0;
		Integer[] arr = new Integer[n];
		Map<Integer, Long> d = new TreeMap<>();
		ArrayDeque<Integer> q = new ArrayDeque<>();
		ArrayList<Integer> res_s = new ArrayList<>();

		for(int i =0; i < n; i++) {arr[i] = input.nextInt();} 
	
		for(int i = 0; i< n; i++)
		{
			d.put( arr[i], (long)(0));
			q.addFirst(arr[i]);
			
			// out.println("adding: "+ arr[i]);
		}

		while(!q.isEmpty())
		{
			if(res_s.size() == m) break;

			int coord = q.pop();
			long dist_temp = d.get(coord); 
			
			// out.println("kir: "+ q);

			if( dist_temp != 0)
			{
				s_distance += dist_temp;
				res_s.add(coord);
			}

			Long distm1, distp1;
			// distp1 = distm1 = null;

			// if(d.get(coord-1)!= null) 
			distm1 = d.get(coord-1);
			// if(d.get(coord+1)!= null)
			 distp1 = d.get(coord+1);

			if(distm1 == null || (distm1 != null && distm1 != 0 && distm1 > dist_temp +1))
			{
				d.put( coord-1 , dist_temp + 1);
				q.add(coord-1);
			}
			if(distp1 == null ||(distp1 != null && distp1 != 0 && distp1 > dist_temp +1))
			{
				d.put( coord+1 , dist_temp + 1);
				q.add(coord+1);
			}
		}

		out.println(s_distance);

		for(Integer it:res_s)
		{
			out.print(it+ " ");
		}
		out.println();

	}
}