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.*;
import java.io.*;
import java.math.*;
import java.lang.*;
public class MyClass {
    public static void main(String[] args) throws Exception {
        Scanner sc=new Scanner(System.in);
        PrintWriter pw=new PrintWriter(System.out);
        int n=sc.nextInt();
        int m=sc.nextInt();
        long[] a=new long[n];
        HashSet<Long> res=new HashSet<>();
        for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
        Queue<Long> q=new LinkedList<>();
        HashMap<Long,Long> hm=new HashMap<>();
        long ans=0L;
        for(int i=0;i<n;i++) {
            q.add(a[i]);
            hm.put(a[i],0L);
        }
        while(!q.isEmpty()) {
            if(res.size()==m)
                break;
            long cur=q.poll();
            if(hm.get(cur)!=0) {
                res.add(cur);
                ans+=hm.get(cur);
            }
            if(!hm.containsKey(cur-1)) {
                hm.put(cur-1,hm.get(cur)+1);
                q.add(cur-1);
            }
            if(!hm.containsKey(cur+1)) {
                hm.put(cur+1,hm.get(cur)+1);
                q.add(cur+1);
            }
        }
        pw.println(ans);
        for(long x:res)
            pw.print(x+" ");
        pw.close();
    }
}