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.*;

public class vc3 {

	public static void main(String[] args) 
	{ 
      Scanner scn=new Scanner(System.in);
      int n=scn.nextInt();
      int m=scn.nextInt();
      	HashMap<Integer,Long>dis=new HashMap();
      	Queue<Integer>que=new LinkedList();
      	int[]ans=new int[m];
//      TreeSet<Long>set=new TreeSet();
//      TreeSet<Long>clone=new TreeSet();
      for(int i=0;i<n;i++) {
    	  int num=scn.nextInt();
    	  dis.put(num,(long)0);
    	  que.add(num);
      }
     n=0;long min=(long)0;
      while(!que.isEmpty()) {
    	  int num=que.poll();
    	  if(n==m)
    		  break;
    	  if(dis.get(num)!=0) {
    		  ans[n]=num;
    		  min+=dis.get(num);
    		  n++;
    	  }
    	  if(!dis.containsKey(num+1)) {
    		  dis.put(num+1, dis.get(num)+1);
    		  que.add(num+1);
    	  }
    	  if(!dis.containsKey(num-1)) {
    		  dis.put(num-1, dis.get(num)+1);
    		  que.add(num-1);
	    	  }
      }
      System.out.println(min);
      for(int t:ans)
    	  System.out.print(t+" ");
	}}