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 ChristmasTrees {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int m = s.nextInt();
        int arr[]  = new int[m];
        Map<Integer, Integer> map  = new HashMap<>();
        Queue<Integer> q = new LinkedList<>();
        long res = 0;
        int index = -1;
        for(int i = 0; i < n; i++) {
            int val = s.nextInt();
            map.put(val, 0);
            q.offer(val);
        }
        while(!q.isEmpty()) {
            int curr = q.poll();
            if(!map.containsKey(curr-1)) {
                if(++index == m) {
                    break;
                }
                int val = map.get(curr) + 1;
                res += val;
                map.put(curr-1, val);
                arr[index] = curr-1;
                q.offer(curr-1);
            }
            if(!map.containsKey(curr+1)) {
                if(++index == m) {
                    break;
                }
                int val = map.get(curr) + 1;
                res += val;
                map.put(curr+1, val);
                arr[index] = curr+1;
                q.offer(curr+1);
            }
        }
        System.out.println(res);
        for(int i = 0; i < m; i++) {
            System.out.print(arr[i] + " ");
        }
    }
}