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  gym{
	static class node{
		int u,dist;
		node(int v,int d){u=v;dist=d;}
	}
	public static void main(String[] args) throws Exception{
		MScanner sc=new MScanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt(),m=sc.nextInt();
		int[]in=sc.takearr(n);
		HashSet<Integer>taken=new HashSet<Integer>();
		LinkedList<node>q=new LinkedList<node>();
		for(int i=0;i<n;i++) {
			taken.add(in[i]);
		}
		for(int i=0;i<n;i++) {
			if(!taken.contains(in[i]-1)) {
				q.add(new node(in[i]-1,1));
				taken.add(in[i]-1);
			}
			if(!taken.contains(in[i]+1)) {
				q.add(new node(in[i]+1,1));
				taken.add(in[i]+1);
			}
		}
		int c=0;
		StringBuilder print=new StringBuilder();
		long ans=0;
		while(c<m && q.size()<m) {
			node cur=q.removeFirst();ans+=cur.dist;
			print.append(cur.u+" ");
			c++;
			if(!taken.contains(cur.u-1)) {
				q.add(new node(cur.u-1,cur.dist+1));
				taken.add(cur.u-1);
			}
			if(!taken.contains(cur.u+1)) {
				q.add(new node(cur.u+1,cur.dist+1));
				taken.add(cur.u+1);
			}
		}
		while(c<m) {
			node cur=q.removeFirst();ans+=cur.dist;
			print.append(cur.u+" ");
			c++;
			if(!taken.contains(cur.u-1)) {
				q.add(new node(cur.u-1,cur.dist+1));
				taken.add(cur.u-1);
			}
			if(!taken.contains(cur.u+1)) {
				q.add(new node(cur.u+1,cur.dist+1));
				taken.add(cur.u+1);
			}
		}
		pw.println(ans);
		pw.println(print);
		pw.flush();
	}
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] takearr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] takearrl(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public Integer[] takearrobj(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] takearrlobj(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}