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.util.Map.Entry;
     
    public class B {
        public static void main(String[] args) {
            Scanner in = new Scanner(System.in);
            int n = in.nextInt();
            int m = in.nextInt();
            ArrayDeque<Integer> q = new ArrayDeque<>();
            HashMap<Integer, Integer> map = new HashMap<>();
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                q.add(x);
                map.put(x, 0);
            }
            ArrayList<Integer> list = new ArrayList<>();
            while (!q.isEmpty() && list.size() < m) {
                int x = q.poll();
                if (map.get(x) != 0) {
                    list.add(x);
                }
                if (!map.containsKey(x + 1)) {
                    q.add(x + 1);
                    map.put(x + 1, map.get(x) + 1);
                }
                if (!map.containsKey(x - 1)) {
                    q.add(x - 1);
                    map.put(x - 1, map.get(x) + 1);
                }
            }
            long sum = 0;
            StringBuilder sb = new StringBuilder();
            for (int i : list) {
                sum += map.get(i);
                sb.append(i + " ");
            }
            System.out.println(sum);
            System.out.println(sb.toString());
     
        }
    }