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.HashMap;
import java.util.LinkedList;
import java.util.Scanner;
 
public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		LinkedList<Integer> q = new LinkedList<Integer>();
		int[] a = new int[n];
		int[] s = new int[m];
 
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		for(int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			q.addLast(a[i]);
			map.put(a[i], 0);
		}
		int p = 0;
		long sum = 0;
		while(p < m) {
			int curr = q.removeFirst();
			
			if(map.get(curr) != 0) {
				s[p] = curr;
				p++;
				sum+= Math.abs(map.get(curr));
			}
			if(!map.containsKey(curr-1)){
				map.put(curr-1, map.get(curr)+1);
			    q.addLast(curr-1);
			}
			if(!map.containsKey(curr+1)){
				map.put(curr+1, map.get(curr)+1);
			    q.addLast(curr+1);
			}
 
		}
		
		System.out.println(sum);
		for(int i = 0; i < m; i++) {
			System.out.print(s[i]+" ");
		}
	
	}
	
}