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.ArrayDeque;
import java.util.HashSet;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;

public class ChristmanTrees {
    private static class PersonWithDist {
        private final int person;
        private final int dist;

        public PersonWithDist(int person, int dist) {
            this.person = person;
            this.dist = dist;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int treesNum = scanner.nextInt();
        int pplNum = scanner.nextInt();
        int[] trees = new int[treesNum];
        for (int t = 0; t < treesNum; t++) {
            trees[t] = scanner.nextInt();
        }
        Set<Integer> visited = new HashSet<>();
        Queue<PersonWithDist> q = new ArrayDeque<>();
        for (int t = 0; t < treesNum; t++) {
            visited.add(trees[t]);
            q.add(new PersonWithDist(trees[t], 0));
        }
        int[] ppl = new int[pplNum];
        int added = 0;
        long totalDist = 0;
        while (!q.isEmpty() && added < pplNum) {
            PersonWithDist curr = q.remove();
            if (!visited.contains(curr.person-1)) {
                visited.add(curr.person-1);
                q.add(new PersonWithDist(curr.person-1, curr.dist+1));
                ppl[added++] = curr.person-1;
                totalDist += curr.dist+1;
            }
            if (added == pplNum) {
                break;
            }
            if (!visited.contains(curr.person+1)) {
                visited.add(curr.person+1);
                q.add(new PersonWithDist(curr.person+1, curr.dist+1));
                ppl[added++] = curr.person+1;
                totalDist += curr.dist+1;
            }
        }
        System.out.println(totalDist);
        StringBuilder sb = new StringBuilder();
        for (int p = 0; p < pplNum; p++) {
            sb.append(ppl[p]).append(' ');
        }
        System.out.println(sb.toString());
    }
}