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.IOException;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.MathContext;
import java.text.DecimalFormat;
import java.util.*;

public class contest {

	public static void main(String[] args) throws IOException{
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] trees = new int[n];
		HashSet<Integer> v= new HashSet<>();
		Queue<Integer> q = new LinkedList<>();
		Queue<Integer> d = new LinkedList<>();
		for(int i=0;i<n;i++) {
			trees[i] = sc.nextInt();
			q.add(trees[i]);
			v.add(trees[i]);
			d.add(0);
		}
		int mt = m;
		Queue<Integer> result = new LinkedList<>();
		Queue<Integer> dres = new LinkedList<>();
		while(!q.isEmpty()&&mt>0) {
			int tr = q.poll();
			int dd = d.poll();
			if(!v.contains(tr-1)) {
				q.add(tr-1);
				d.add(dd+1);
				result.add(tr-1);
				dres.add(dd+1);
				v.add(tr-1);
				mt--;
			}
			if(!v.contains(tr+1)) {
				q.add(tr+1);
				d.add(dd+1);
				result.add(tr+1);
				dres.add(dd+1);
				v.add(tr+1);
				mt--;
			}
		}
		long res = 0;
		for(int i=0;i<m;i++) {
			res+=dres.poll();
		}
		pw.println(res);
		for(int i=0;i<m;i++) {
			pw.print(result.poll() + " ");
		}
		pw.println();
		pw.flush();
		pw.close();
	}
}