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 CodeforcesContest {

    private static void sport(Set<Integer> trees, int n) {
        long ans = 0;
        Set<Integer> set = new HashSet<>();
        set.addAll(trees);
        Queue<int[]> queue = new LinkedList<>();
        for (int tree : trees) {
            queue.add(new int[]{tree, 0});
        }
        while (n > 0 && !queue.isEmpty()) {
            int[] tree = queue.poll();
            if (n > 0 && !set.contains(tree[0] - 1)) {
                set.add(tree[0] - 1);
                queue.add(new int[]{tree[0] - 1, tree[1] + 1});
                n--;
                ans += tree[1]+1;
            }
            if (n > 0 && !set.contains(tree[0] + 1)) {
                set.add(tree[0] + 1);
                queue.add(new int[]{tree[0] + 1, tree[1] + 1});
                n--;
                ans += tree[1]+1;
            }
        }
        System.out.println(ans);
        for (Integer integer : set) {
            if (trees.contains(integer)){
                continue;
            }
            System.out.print(integer + " ");
        }
    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        int people = sc.nextInt();
        Set<Integer> trees = new HashSet<>();
        for (int i = 0; i < t; i++) {
            trees.add(sc.nextInt());
        }
        sport(trees, people);
    }
}