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 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = 1;
        while (t-->0) {
            int n = in.nextInt();
            int m = in.nextInt();

            HashSet<Integer> set = new HashSet<>();
            ArrayDeque<Pair> q = new ArrayDeque<>();
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt();
                set.add(x);
                if (!set.contains(x - 1)) {
                    q.offer(new Pair(x - 1, -1, 1));
                }
                
                if (!set.contains(x + 1)) {
                    q.offer(new Pair(x + 1, 1, 1));
                }
            }

            ArrayList<Integer> li = new ArrayList<>();
            long sum = 0;
            for (int j = 0; j < m; ++j) {
                while (!q.isEmpty()) {
                    Pair p = q.poll();
                    if (!set.contains(p.f)) {
                        set.add(p.f);
                        li.add(p.f);
                        sum += p.d;
                        q.offer(new Pair (p.f + p.s, p.s, p.d + 1));
                        break;
                    }
                }
            }

            System.out.println(sum);
            for (int i : li) {
                System.out.print(i+ " ");
            } System.out.println();
        }
    }
}
class Pair implements Comparable<Pair> {
    int f, s, d;

    public Pair(int f, int s, int d) {
        this.f = f;
        this.s = s;
        this.d = d;
    }

    @Override
    public String toString() {
        return this.f + ", " + this.s;
    }

    @Override 
    public int compareTo(Pair p) {
        if (this.f == p.f)
            return this.s - p.s;
        
        return this.f - p.f;
    }
}