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 void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        long ans = 0;
        Set<Long> trees = new HashSet<>();
        Set<Long> used = new HashSet<>();
        List<Long> q = new ArrayList();
        int qp = 0;
        long time = System.currentTimeMillis();
        for (int i = 0; i < n; i++) {
            trees.add(sc.nextLong());
        }
        used.addAll(trees);
        for (long t : trees) {
            q.add(t);
            q.add(0L);
        }

        while (qp < q.size()) {
            long t = q.get(qp++);
            long d = q.get(qp++);

            if (!used.contains(t) || d == 0) {
                used.add(t);
                ans += d;
                q.add(t+1);
                q.add(d+1);
                q.add(t-1);
                q.add(d+1);
            }
            if (used.size() == n + m) break;
        }

        //System.out.println(used.size());
        System.out.println(ans);
        StringBuilder sb = new StringBuilder();
        for (long p : used) {
            if (!trees.contains(p)) sb.append(p).append(" ");
        }
        System.out.print(sb.toString());

    }
}