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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class christmastrees {

	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

		StringTokenizer st = new StringTokenizer(in.readLine());
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		
		HashSet<Integer> v = new HashSet<Integer>();
		LinkedList<Integer> q = new LinkedList<Integer>();
		TreeSet<Integer> t = new TreeSet<Integer>();
		
		StringTokenizer st1 = new StringTokenizer(in.readLine());
		for (int i = 0; i < n; i++) {
			int num = Integer.parseInt(st1.nextToken());
			q.add(num);
			v.add(num);
			t.add(num);
		}
		
		ArrayList<Integer> res = new ArrayList<Integer>();
		
		while(!q.isEmpty()) {
			int curr = q.poll();
			
			if(!v.contains(curr+1)) {
				v.add(curr+1);
				q.add(curr+1);
				res.add(curr+1);
			}
			
			if(!v.contains(curr-1)) {
				v.add(curr-1);
				q.add(curr-1);
				res.add(curr-1);
			}
			
			if(res.size() >= m)
				break;
		}
		
		if(res.size() > m) {
			long max = 0;
			int ind = 0;
			for(int i = 0; i < res.size(); i++) {
				int curr = res.get(i);
				long l = (t.lower(curr) == null) ? Long.MAX_VALUE : (long) (t.lower(curr) - curr);
				long h = (t.higher(curr) == null) ? Long.MAX_VALUE : (long) (t.higher(curr) - curr);
				long dist = Math.min(Math.abs(l), Math.abs(h));
				if(dist > max) {
					max = dist;
					ind = i;
				}
			}
			res.remove(ind);
		}
		
		long total = 0;
		for(int i = 0; i < res.size(); i++) {
			int curr = res.get(i);
			long l = (t.lower(curr) == null) ? Long.MAX_VALUE : (long) (t.lower(curr) - curr);
			long h = (t.higher(curr) == null) ? Long.MAX_VALUE : (long) (t.higher(curr) - curr);
			long dist = Math.min(Math.abs(l), Math.abs(h));
			total += dist;
		}
		
		out.println(total);
		
		for(int i = 0; i < res.size(); i++) {
			int curr = res.get(i);
			out.print(curr + " ");
		}

		in.close();
		out.close();
	}

	
}
