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 = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        int[] x = new int[n];
        HashSet<Long> set = new HashSet<Long>();
        ArrayDeque<long[]> queue = new ArrayDeque<long[]>();
        for (int i=0;i<n;i++) {
            x[i] = Integer.parseInt(sc.next());
            set.add((long)x[i]);
            long[] add_1 = {x[i]+1, 1, 1}; // position direction distance
            long[] add_2 = {x[i]-1, -1, 1};
            queue.add(add_1);
            queue.add(add_2);
        }

        int cnt = 0;
        HashSet<Long> ans = new HashSet<Long>();
        long dist = 0;
        while (cnt<m) {
            long[] rem = queue.remove();
            if (set.contains(rem[0])) continue;
            set.add(rem[0]);
            ans.add(rem[0]);
            dist += rem[2];
            cnt++;
            long[] add = {rem[0]+rem[1], rem[1], rem[2]+1};
            queue.add(add);
        }
        System.out.println(dist);
        ArrayList<Long> list = new ArrayList<Long>(ans);
        for (int i=0;i<m;i++) {
            if (i==m-1) {
                System.out.println(list.get(i));
            } else {
                System.out.print(list.get(i)+" ");
            }
        }
    }
}