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.math.BigInteger;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        //Scanner f = new Scanner(new File("uva.in"));
        //Scanner f = new Scanner(System.in);
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(f.readLine());
        LinkedList<Integer> queue = new LinkedList<>();
        HashSet<Integer> taken = new HashSet<>();
        for(int i = 0; i < n; i++) {
            int x = Integer.parseInt(st.nextToken());
            queue.offer(x);
            taken.add(x);
        }
        ArrayList<Integer> people = new ArrayList<>();
        int placed = 0;
        int distance = 0;
        long totalDistance = 0;
        while(placed < m) {
            int size = queue.size();
            distance++;
            for(int i = 0; i < size; i++) {
                int temp = queue.poll();
                if(!taken.contains(temp-1) && placed < m) {
                    placed++;
                    totalDistance += distance;
                    queue.offer(temp-1);
                    taken.add(temp-1);
                    people.add(temp-1);
                }
                if(!taken.contains(temp+1) && placed < m) {
                    placed++;
                    totalDistance += distance;
                    queue.offer(temp+1);
                    taken.add(temp+1);
                    people.add(temp+1);
                }
            }
        }
        out.println(totalDistance);
        out.print(people.get(0));
        for(int i = 1; i < m; i++) {
            out.print(" " + people.get(i));
        }
        out.println();
        f.close();
        out.close();
    }
}
