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 
////////////////////---------------------------SHUBHAM CHAUDHARI-------------------------------///////////////////////

import java.util.*;

public class Main {

    static long min=Long.MAX_VALUE;
    static long m=1000000007L;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        int m=in.nextInt();
        Queue<Long>q=new LinkedList<>();
        HashMap<Long,Long>map=new HashMap<>();
        long ans[]=new long[m];
        for(int i=0;i<n;i++)
        {
            long x=in.nextLong();
            ((LinkedList<Long>) q).add(x);
            map.put(x,0L);
        }
        n=0;
        long min=0;
        while (!q.isEmpty()&&n<m)
        {
            long num=q.poll();
            if(map.get(num)!=0)
            {
                ans[n]=num;
                min+=map.get(num);
                n++;
            }
            if(!map.containsKey(num+1))
            {
                ((LinkedList<Long>) q).add(num+1);
                map.put(num+1,map.get(num)+1);
            }
            if(!map.containsKey(num-1))
            {
                ((LinkedList<Long>) q).add(num-1);
                map.put(num-1,map.get(num)+1);
            }
        }
        System.out.println(min);
        StringBuilder res=new StringBuilder();
        for(int i=0;i<m;i++)
        {
            res.append(ans[i]+" ");
        }
        System.out.println(res);
    }

}