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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class D_Christmas_Tree {
	
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
	    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	    int N = sc.nextInt();
	    int M = sc.nextInt();
	    
	    HashSet<Integer> trees = new HashSet<Integer>();
	    PriorityQueue<Node> pq = new PriorityQueue<Node>();
	    for(int i = 0; i < N; i++) {
	    	int tree_loc = sc.nextInt();
	    	trees.add(tree_loc);
	    	pq.add(new Node(tree_loc, 0));
	    }
	    
	    //Mark if location has been visited
	    HashSet<Integer> visited = new HashSet<>();
	    ArrayList<Integer> locations = new ArrayList<>();
	    long ans = 0;
	    while(locations.size() < M) {
	    	Node min = pq.poll();
	    	
	    	//If we aren't at original tree or visited node
	    	assert(!visited.contains(min.loc)): "visited value reached";
	    	if(min.dist != 0) {
	    		visited.add(min.loc);
	    		ans += min.dist;
	    		locations.add(min.loc);
	    	}
	    	
    		//If left neighbor not a tree & not visited
    		if(!trees.contains(min.loc - 1) && !visited.contains(min.loc - 1)) {
    			pq.add(new Node(min.loc - 1, min.dist + 1));
    			visited.add(min.loc - 1);
    		}
    		
    		//If right neighbor not a tree & not visited
    		if(!trees.contains(min.loc + 1) && !visited.contains(min.loc + 1)) {
    			pq.add(new Node(min.loc + 1, min.dist + 1));
    			visited.add(min.loc + 1);
    		}
	    }
	    
	    out.println(ans);
	    for(int loc : locations) {
	    	out.print(loc + " ");
	    }
	    out.println();
	    
	    out.close();
	}
	
	static class Node implements Comparable<Node> {
		int loc = 0;
		int dist = 0;
		
		Node(int loc, int dist) {
			this.loc = loc;
			this.dist = dist;
		}


		@Override
		public int compareTo(Node o) {
			return Integer.compare(this.dist, o.dist);
		}
		
		
	}
	
	public static class MyScanner {
		BufferedReader br;
	    StringTokenizer st;
	 
	    public MyScanner() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	    }
	 
	    String next() {
	    	while (st == null || !st.hasMoreElements()) {
	    		try {
	    			st = new StringTokenizer(br.readLine());
	            	
	    		} catch (IOException e) {
	    			e.printStackTrace();
	            }
	          }
	    	return st.nextToken();
	   }
	 
	   int nextInt() {
		   return Integer.parseInt(next());
	   }
	 
	   long nextLong() {
		   return Long.parseLong(next());
	   }
	 
	   double nextDouble() {
		   return Double.parseDouble(next());
	   }
	 
	   String nextLine(){
		   String str = "";
		   try {
			   str = br.readLine();
		   } catch (IOException e) {
			   e.printStackTrace();
		   }
		   return str;
	   }
	}
}