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.*;

/**
 * @author 超厉害的我啊
 * @date 2020/9/9 08:09:00
 */

public class Main {
    static int n,m;
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int p = sc.nextInt();
        int arr[] = new int[n];
        for(int i=0;i<n;i++) {
            arr[i] = sc.nextInt();
        }
        func(arr,n,p);
    }
    static void func(int arr[],int n,int p) {
        Queue<Integer> que = new LinkedList<>();
        HashMap<Integer,Integer> hm = new HashMap<>();
        ArrayList<Integer> ans = new ArrayList<>();

        for(int i=0;i<n;i++) {
            hm.put(arr[i],0);
            que.add(arr[i]);
        }
        long res = 0;
        while(!que.isEmpty()) {
            if(ans.size()==p) break;
            int k = que.poll();
            if(hm.get(k)!=0) {
                res+=hm.get(k);
                ans.add(k);
            }
            if(!hm.containsKey(k-1)) {
                hm.put(k-1,hm.get(k)+1);
                que.add(k-1);
            }
            if(!hm.containsKey(k+1)) {
                hm.put(k+1,hm.get(k)+1);
                que.add(k+1);
            }
        }
        System.out.println(res);
        for(int i=0;i<p;i++) {
            System.out.print(ans.get(i)+" ");
        }
    }

}

	 	 	    				 		    				 				