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.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 	public InputReader(InputStream st) {
            this.stream = st;
	} 
	public int read() {
            if (snumChars == -1)
	 	throw new InputMismatchException();
            if (curChar >= snumChars) {
		curChar = 0;
                try {
                    snumChars = stream.read(buf);
		} 
                catch (IOException e) {
                    throw new InputMismatchException();
           	}
		if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
	}
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
               	c = read();
            }
            int sgn = 1;
            if (c == '-') {
		sgn = -1;
		c = read();
            }
            int res = 0;
            do {
		res *= 10;
		res += c - '0';
		c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
	} 
	public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
	} 
	public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
		a[i] = ni();
            }
            return a;
	} 
	public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
		c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
		res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
	}
	public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
		c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
	public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
	} 
    }
    static PrintWriter w = new PrintWriter(System.out);
    static long mod=998244353L;
    
    public static void main (String[] args)throws IOException{
        InputReader sc=new InputReader(System.in);	 
        int n=sc.ni(),m=sc.ni();
        TreeSet<Integer> set=new TreeSet<Integer>();
        TreeSet<Integer> rem=new TreeSet<Integer>();
        TreeSet<Integer> ans=new TreeSet<Integer>();
        //int arr[]=new int[n];
        for(int i=0;i<n;i++){
            int a=sc.ni();
            set.add(a);
            rem.add(a-1);
            rem.add(a+1);
        }
        for(int i:set)rem.remove(i);
        int p=0;
        long res=0;
        while(ans.size()<m){
            p++;
            TreeSet<Integer> te=new TreeSet<Integer>();
            TreeSet<Integer> te1=new TreeSet<Integer>();
            for(int i:rem){
                res+=(long)p;
                ans.add(i);
                te1.add(i);
                if(ans.size()>=m)break;
                if(!set.contains(i+1)&&!ans.contains(i+1)){
                    te.add(i+1);
                }
                if(!set.contains(i-1)&&!ans.contains(i-1)){
                    te.add(i-1);
                }
            }
            //for(int i:te1)rem.remove(i);
            for(int i:te)rem.add(i);
            for(int i:te1)rem.remove(i);
        }
        w.println(res);
        for(int i:ans)w.print(i+" ");
        w.println();
    	w.close();
    }
}