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.LinkedList; 
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.*;
public class Main {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] cmd=br.readLine().split(" ");
		int n=Integer.valueOf(cmd[0]);
		int m=Integer.valueOf(cmd[1]);
		long[] arr=new long[n];
		cmd=br.readLine().split(" ");
		for(int i=0;i<n;i++)
		{
			arr[i]=Long.valueOf(cmd[i]);
		}
		HashMap<Long,Long> map=new HashMap<>();
		Queue<Long> qu=new LinkedList<>();
		for(int i=0;i<n;i++)
		{
			map.put(arr[i],(long)0);
			qu.add(arr[i]);
		}
		long ans=0;
		ArrayList<Long> res=new ArrayList<>();
		while(qu.size()!=0)
		{
			if(res.size()==m)
				break;
			long x=qu.poll();
			if(map.get(x)!=0)
			{
				res.add(x);
				ans=ans+map.get(x);
			}
			if(!map.containsKey(x-1))
			{
				map.put(x-1,map.get(x)+1);
				qu.add(x-1);
			}
			if(!map.containsKey(x+1))
			{
				map.put(x+1,map.get(x)+1);
				qu.add(x+1);
			}
		}
		System.out.println(ans);
		for(int i=0;i<m;i++)
		{
			System.out.print(res.get(i)+" ");
		}
		System.out.println();
	}

}
