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.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Random;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;
 
public class Solution {
    public static void main(String[] args){
    	Scanner in = new Scanner(System.in);
    	int n = in.nextInt();
    	int m = in.nextInt();
    	int k = 0;
    	long min = 0;
    	Set<Integer> people = new TreeSet<Integer>();
    	Set<Integer> trees = new TreeSet<Integer>();
    	Set<Integer> next = new TreeSet<Integer>();
    	for(int i = 0; i < n; ++i){
    		int l = in.nextInt();
    		trees.add(l);
    	}
    	int p = 1;
    	for(Integer i : trees){
    		if(!trees.contains(i+1) && !people.contains(i+1)){
    			min = min + p;
    			next.add(i+1);
    			people.add(i+1);
    			++k;
    		}
    		if(k >= m)
    			break;
    		if(!trees.contains(i-1) && !people.contains(i-1)){
    			min = min + p;
    			next.add(i-1);
    			people.add(i-1);
    			++k;
    		}
    		if(k >= m)
    			break;
    	}
    	while(k < m){
    		Set<Integer> next2 = new TreeSet<>();
    		next2 = next;
    		next = new TreeSet<Integer>();
        	++p;
        	for(Integer i : next2){
        		if(!trees.contains(i+1) && !people.contains(i+1)){
        			min = min + p;
        			next.add(i+1);
        			people.add(i+1);
        			++k;
        		}
        		if(k >= m)
        			break;
        		if(!trees.contains(i-1) && !people.contains(i-1)){
        			min = min + p;
        			next.add(i-1);
        			people.add(i-1);
        			++k;
        		}
        		if(k >= m)
        			break;
        	}
    	}
    	System.out.println(min);
    	for(Integer i : people)
    		System.out.print(i+" ");
    }
}