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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Queue;

public class N {
	public static void main(String[] args) throws IOException {
		StreamTokenizer st = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
		st.nextToken();
		int n = (int) st.nval;
		st.nextToken();
		int m = (int) st.nval;
		long[] a = new long[n];
		HashMap<Long, Long> map = new HashMap();
		Queue<Long> q = new LinkedList<Long>();
		ArrayList<Long> arr = new ArrayList();
		for (int i = 0; i < n; i++) {
			st.nextToken();
			a[i] = (int) st.nval;
			map.put(a[i], (long) 0);
			q.add(a[i]);
		}
		long x = 0;
		while (!q.isEmpty()) {

			if (arr.size() == m)
				break;
			long k = q.poll();
			if (map.get(k) != 0) {
				arr.add(k);
				x += map.get(k);
			}

			if (!map.containsKey(k - 1)) {
				map.put(k - 1, map.get(k) + 1);
				q.add(k - 1);
			}

			if (!map.containsKey(k + 1)) {
				map.put(k + 1, map.get(k) + 1);
				q.add(k + 1);

			}

		}
		System.out.println(x);
		for (int i = 0; i < m; i++)
			System.out.print(arr.get(i) + " ");
	}
}

 		 		    	   		  		  	 		 		