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 
/* Rajkin Hossain */

import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class D{
   
    FastInput k = new FastInput(System.in);
    //FastInput k = new FastInput("/home/rajkin/Desktop/input.txt");
    FastOutput z = new FastOutput();
    
    int n, m;
    TreeSet<Integer> set;
    
    HashSet<Integer> human, tree;
    
    Pair [] y;
    
    int [] yy;
    
    boolean isCovered(int l) {
    	return human.contains(l) || tree.contains(l);
    }
    
    boolean ok(int key) {
    	Integer h = set.higher(key);
    	if(h == null) return true;
    	
    	int r = y[key].r + 1;
    	if(Math.abs(h-r) < Math.abs(key-r)) {
    		return true;
    	}
    	
    	return true;
    }
    
    void startAlgo() {
    	
    	int start = -1;
    	long sum = 0;
    	
    	while(!set.isEmpty()) {
    		Integer key = set.higher(start);
    		
    		if(key == null) {
    			key = set.first();
    		}
    		
    		int l = y[key].l - 1;
    		int r = y[key].r + 1;
    		
    		if(isCovered(l) && isCovered(r)) {
    			set.remove(key);
    			
    			continue;
    		}
    		
    		if(!isCovered(l)){
    			human.add(l);
    			sum += Math.abs(l-yy[key]);
    			y[key].l = l;
    		}
    		
    		if(human.size() == m) break;
    		
    		if(!isCovered(r)) {
    			human.add(r);
    			y[key].r = r;
    			sum += Math.abs(r-yy[key]);
    		}
    		
    		if(human.size() == m) break;
    		
    		start = key;
    	}
    	
    	z.println(sum);
    	
    	for(int ans : human) {
    		z.print(ans+" ");
    	}
    	
    	z.println();
    }
    
    void startProgram() {
    	
    	while(k.hasNext()) {
    		set = new TreeSet<Integer>();
    		
    		human = new HashSet<Integer>();
    		tree = new HashSet<Integer>();
    		
    		n = k.nextInt();
    		m = k.nextInt();
    		
    		y = new Pair[n + 1];
    		yy = new int[n + 1];
    		
    		for(int i = 1; i<=n; i++) {
    			int v = k.nextInt();
    			
    			tree.add(v);
    			set.add(i);
    			
    			y[i] = new Pair(v, v);
    			
    			yy[i] = v;
    		}
    		
    		startAlgo();
    	}
    	
    	z.flush();
    	System.exit(0);
    }
    
    class Pair {
    	int l, r;

		public Pair(int l, int r) {
			super();
			this.l = l;
			this.r = r;
		}	
    }
    
    public static void main(String [] args) throws IOException {
        new Thread(null, new Runnable(){
            public void run(){
            	try{ 
            		new D().startProgram();
            	}
            	catch(Exception e){
            		e.printStackTrace();
            	}
            }
        },"Main",1<<28).start();
    }
    
    static class Template {
    	
    	static <E> HashSet<E> generateSet(E [] y) {
    		HashSet<E> set = new HashSet<E>();
    		
    		for(E key : y) {
    			set.add(key);
    		}
    		
    		return set;
    	}
    	
    	static <E> HashMap<E, Integer> generateCountMap(E [] y) {
    		HashMap<E, Integer> map = new HashMap<E, Integer>();
    		
    		for(E key : y) {
    			map.putIfAbsent(key, 0);
    			map.put(key, map.get(key) + 1);
    		}
    		
    		return map;
    	}
    }

    /* MARK: FastInput and FastOutput */
 
    class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        FastInput(InputStream stream){
            reader = new BufferedReader(new InputStreamReader(stream));
        }
       
        FastInput(String path){
            try {
                reader = new BufferedReader(new FileReader(path));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            tokenizer = null;
        }
 
        String next() {
            return nextToken();
        }
       
        String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
           
            return null;
        }
 
        boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        long nextLong() {
            return Long.valueOf(nextToken());
        }
        
        int [] getInputIntArray(int n) {
        	
        	int [] input = new int[n];
        	
        	for(int i = 0; i<n; i++) {
        		input[i] = nextInt();
        	}
        	
        	return input;
        }
        
        long [] getInputLongArray(int n) {
        	
        	long [] input = new long[n];
        	
        	for(int i = 0; i<n; i++) {
        		input[i] = nextLong();
        	}
        	
        	return input;
        }
        
        int [] getInputIntArrayOneBasedIndex(int n) {
        	
        	int [] input = new int[n+1];
        	
        	for(int i = 1; i<=n; i++) {
        		input[i] = nextInt();
        	}
        	
        	return input;
        }
        
        long [] getInputLongArrayOneBasedIndex(int n) {
        	
        	long [] input = new long[n+1];
        	
        	for(int i = 1; i<=n; i++) {
        		input[i] = nextLong();
        	}
        	
        	return input;
        }
        
        <E> void fill2DArray(E [][] array, E value) {
        	for(int i = 0; i<array.length; i++) {
            	for(int j = 0; j<array[0].length; j++) {
            		array[i][j] = value;
            	}
        	}
        }
        
        <E> void fill3DArray(E [][][] array, E value) {
        	for(int i = 0; i<array.length; i++) {
            	for(int j = 0; j<array[0].length; j++) {
                	for(int k = 0; k<array[0][0].length; k++) {
                		array[i][j][k] = value;
                	}
            	}
        	}
        }
        
        <E> void fill4DArray(E [][][][] array, E value) {
        	for(int i = 0; i<array.length; i++) {
            	for(int j = 0; j<array[0].length; j++) {
                	for(int k = 0; k<array[0][0].length; k++) {
                    	for(int l = 0; l<array[0][0][0].length; l++) {
                    		array[i][j][k][l] = value;
                    	}
                	}
            	}
        	}
        }
    }
 
    class FastOutput extends PrintWriter {
		FastOutput() {
			super(new BufferedOutputStream(System.out)); 
		}
		
		public void debug(Object...obj) {
		    System.err.println(Arrays.deepToString(obj));
		}
    }
}
