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.io.*;
import java.util.*;

public class ChristmasTrees{
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String st[] =  br.readLine().split(" ");

		int n =  Integer.parseInt(st[0]);
		int m = Integer.parseInt(st[1]);

		HashMap<Integer, Integer> map = new HashMap<>();

		int i;

		Queue<Node> queue = new LinkedList<>();

		st = br.readLine().split(" ");
		int num;

		for(i = 0; i < n; i++){
			num = Integer.parseInt(st[i]);

			map.put(num, 1);
			queue.add(new Node(num, 0));
		}

		int k = 0;

		Node arr[] = new Node[m];

		long sum = 0;

		while(true){
			Node out = queue.remove();

			if(!map.containsKey(out.value+1)){
				Node node = new Node(out.value+1, out.dist + 1);
				queue.add(node);

				arr[k++] = node;

				sum += node.dist;
				map.put(out.value+1, 1);
			}

			if(k == m){
				break;
			}

			if(!map.containsKey(out.value-1)){
				Node node = new Node(out.value-1, out.dist + 1);
				queue.add(node);

				sum += node.dist;
				arr[k++] = node;
				map.put(out.value-1, 1);
			}
			if(k == m){
				break;
			}
		}

		System.out.println(sum);

		System.out.print(arr[0].value);

		for(k = 1; k < m; k++){
			System.out.print(" " + arr[k].value);
		}
	}

	public static class Node{
		int value;
		int dist;

		public Node(int value, int dist){
			this.value = value;
			this.dist = dist;
		}
	}
}