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.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int m=input.nextInt();
            int x[]=new int[n];
            for(int i=0;i<n;i++)
            {
                x[i]=input.nextInt();
            }
            mergeSort(x,0,n-1);
            Queue<Pair> q1=new LinkedList<>();
            Queue<Pair> q2=new LinkedList<>();
            for(int i=0;i<n;i++)
            {
                if(i==0)
                {
                    q1.add(new Pair(Integer.MIN_VALUE,x[i]));
                }
                else
                {
                    if(x[i]-x[i-1]>1)
                    {
                        q1.add(new Pair(x[i-1],x[i]));
                    }
                }
            }
            q1.add(new Pair(x[n-1],Integer.MAX_VALUE));
            long count=0;
            ArrayList<Integer> list=new ArrayList<>();
            int y=1;
            int f=0;
            while(true)
            {
                while(!q1.isEmpty())
                {
                    Pair p=q1.poll();
                    if(p.l==Integer.MIN_VALUE)
                    {
                        list.add(p.r-1);
                        q2.add(new Pair(Integer.MIN_VALUE,p.r-1));
                        count+=y;
                        if(list.size()==m)
                        {
                            f=1;
                            break;
                        }
                    }
                    else if(p.r==Integer.MAX_VALUE)
                    {
                        list.add(p.l+1);
                        q2.add(new Pair(p.l+1,Integer.MAX_VALUE));
                        count+=y;
                        if(list.size()==m)
                        {
                            f=1;
                            break;
                        }
                    }
                    else
                    {
                        if(p.r-p.l>=3)
                        {
                            list.add(p.l+1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                            list.add(p.r-1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                            q2.add(new Pair(p.l+1,p.r-1));
                        }
                        else if(p.r-p.l==2)
                        {
                            list.add(p.l+1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                        }
                    }
                }
                y++;
                if(f==1)
                {
                    break;
                }
                while(!q2.isEmpty())
                {
                    Pair p=q2.poll();
                    if(p.l==Integer.MIN_VALUE)
                    {
                        list.add(p.r-1);
                        q1.add(new Pair(Integer.MIN_VALUE,p.r-1));
                        count+=y;
                        if(list.size()==m)
                        {
                            f=1;
                            break;
                        }
                    }
                    else if(p.r==Integer.MAX_VALUE)
                    {
                        list.add(p.l+1);
                        q1.add(new Pair(p.l+1,Integer.MAX_VALUE));
                        count+=y;
                        if(list.size()==m)
                        {
                            f=1;
                            break;
                        }
                    }
                    else
                    {
                        if(p.r-p.l>=3)
                        {
                            list.add(p.l+1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                            list.add(p.r-1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                            q1.add(new Pair(p.l+1,p.r-1));
                        }
                        else if(p.r-p.l==2)
                        {
                            list.add(p.l+1);
                            count+=y;
                            if(list.size()==m)
                            {
                                f=1;
                                break;
                            }
                        }
                    }
                }
                y++;
                if(f==1)
                {
                    break;
                }
            }
            out.println(count);
            for(int i=0;i<list.size();i++)
            {
                out.print(list.get(i)+" ");
            }
            out.println();
        }
        out.close();
    }
    static class Pair
    {
        int l,r;
        Pair(int l,int r)
        {
            this.l=l;
            this.r=r;
        }
    }
    public static void mergeSort(int a[],int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort(a,p,q);
            mergeSort(a,q+1,r);
            merge(a,p,q,r);
        }
    }
    public static void merge(int a[],int p,int q,int r)
    {
        int n1=q-p+2;
        int L[]=new int[n1];
        int n2=r-q+1;
        int R[]=new int[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a[i];
        }
        L[n1-1]=Integer.MAX_VALUE;
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a[i];
        }
        R[n2-1]=Integer.MAX_VALUE;
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x]<=R[y])
            {
                a[i]=L[x];
                x++;
            }
            else
            {
                a[i]=R[y];
                y++;
            }
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            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;
        }
    }
}