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.io.*;
import java.math.BigInteger;
public class code {
	
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] ss=br.readLine().trim().split(" ");
		int n=Integer.parseInt(ss[0]);
		int m=Integer.parseInt(ss[1]);
		long[] arr=new long[n];
		Queue<Long> queue=new LinkedList<>();
		HashSet<Long> set=new HashSet<>();
		ss=br.readLine().trim().split(" ");
		for(int i=0 ; i<arr.length ; i++) {
			arr[i]=Integer.parseInt(ss[i]);
			set.add(arr[i]);
			queue.add(arr[i]);
		}
		queue.add(null);
		int count=0;
		ArrayList<Long> ans=new ArrayList<>();
		long sum=0;
		long inc=1;
		while(count<m) {
			Long curr=queue.remove();
			if(curr==null) {
				if(queue.isEmpty()) {
					break;
				}
				inc++;
				queue.add(null);
				continue;
			}
			if(!set.contains(curr+1)) {
				set.add(curr+1);
				queue.add(curr+1);
				ans.add(curr+1);
				count++;
				sum+=inc;
				if(count==m) {
					break;
				}
			}
			if(!set.contains(curr-1)) {
				set.add(curr-1);
				queue.add(curr-1);
				ans.add(curr-1);
				count++;
				sum+=inc;
				if(count==m) {
					break;
				}
			}
		}
		System.out.println(sum);
		for(int i=0 ; i<ans.size() ; i++) {
			System.out.print(ans.get(i)+" ");
		}
		System.out.println();
	}
}