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.*;
import java.awt.*;

public class ChristmasTrees {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(f.readLine());
        Queue<Point> q = new LinkedList<Point>();
        HashSet<Integer> s = new HashSet<Integer>();
        int[] x = new int[n];
        for (int i=0; i<n; i++)
        {
            x[i] = Integer.parseInt(st.nextToken());
            s.add(x[i]);
            q.add(new Point(x[i]+1, 1));
            q.add(new Point(x[i]-1, -1));
        }
        ArrayList<Integer>l = new ArrayList<Integer>();
        int count = 0;
        long total = 0;
        while(count<m)
        {
            Point p = q.remove();
            if (s.add(p.x))
            {
                count++;
                l.add(p.x);
                if (p.y>0)
                {
                    total+=(long)p.y;
                    q.add(new Point(p.x+1, p.y+1));
                }
                else
                {
                    total-=(long)p.y;
                    q.add(new Point(p.x-1, p.y-1));
                }
            }
        }
        System.out.println(total);

        for (int i: l)
        {
            System.out.print(i + " ");
        }
        System.out.println();


    }
}
