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.*;
public class C_Tree {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		TreeMap<Integer, Integer> map = new TreeMap<Integer,Integer>();
		Queue<Integer> q = new LinkedList<>();
		for(int i=0;i<n;i++) {
			int y = sc.nextInt();
			map.put(y, 0);
			q.add(y);
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		long ans1 =0;
		
		while(!q.isEmpty()) {
			//System.out.println("anuj");
			if(ans.size()==m) {
				break;
			}
			int curr = q.poll();
			if(map.get(curr)!=0) {
				ans1 = ans1+map.get(curr);
				ans.add(curr);
			}
			if(map.get(curr-1)==null) {
				map.put(curr-1, map.get(curr)+1);
				q.add(curr-1);
			}
			if(map.get(curr+1)==null) {
				map.put(curr+1, map.get(curr)+1);
				q.add(curr+1);
			}
		}
		System.out.println(ans1);
		for(int i=0;i<ans.size();i++) {
			sb.append(ans.get(i)+" ");
		}
		System.out.println(sb);
		
	}

}
