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 
/** https://codeforces.com/problemset/problem/1283/D
 * #bfs #graph #greedy
 */

import java.util.Scanner;
import java.util.Queue;
import java.util.LinkedList;
import java.util.ArrayList;
import java.util.HashSet;
public class ChristmasTrees {
    private static class Node {
        int id, dist;
        Node(int id, int dist) {
            this.id = id;
            this.dist = dist;
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        Queue<Node> q = new LinkedList<>();
        HashSet<Integer> visited = new HashSet<>();
        for (int i = 0; i < n; i++) {
            int id = sc.nextInt();
            visited.add(id);
            q.add(new Node(id, 0));
        }

        long sumDist = 0;
        ArrayList<Integer> people = new ArrayList<>();
        while(!q.isEmpty()) {
            Node node = q.poll();
            int newDist = node.dist + 1;

            for (int i = 0; i < 2; i++) {
                int person = (i == 0) ? (node.id + newDist) : (node.id - newDist);
                if (!visited.contains(person)) {
                    sumDist += newDist;
                    m--;
                    people.add(person);
                    visited.add(person);
                    q.add(new Node(node.id, newDist));
                }
                if (m == 0) {
                    System.out.println(sumDist);
                    people.forEach(x -> System.out.print(x + " "));
                    return;
                }
            }
        }
    }
}