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.*;
import java.lang.reflect.Array;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    Queue<Long> q = new ArrayDeque<>();
    TreeSet<Long> used = new TreeSet<>();
    ArrayList<Long> ans = new ArrayList<>();

    void bfs(int m) {
        int done = 0;
        while (done < m) {
            long v = q.poll();
            if (!used.contains(v + 1)) {
                q.add(v + 1);
                done++;
                used.add(v + 1);
                ans.add(v + 1);
            }
            if (done < m && !used.contains(v - 1)) {
                q.add(v - 1);
                done++;
                used.add(v - 1);
                ans.add(v - 1);
            }
        }
    }

    void run() throws IOException {
        int n = nextInt();
        int m = nextInt();
        TreeSet<Long> ts = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            long x = nextLong();
            ts.add(x);
            q.add(x);
            used.add(x);
        }
        ts.add(Long.MIN_VALUE / 3);
        ts.add(Long.MAX_VALUE / 3);
        long dist = 0;
        bfs(m);
        for (Long c : ans) {
            long left = ts.lower(c);
            long right = ts.ceiling(c);
            dist += min(c - left, right - c);
        }
        pw.println(dist);
        for (Long c : ans) {
            pw.print(c + " ");
        }
        pw.close();
    }

    class Point {
        long x, y;

        public Point(long a, long b) {
            x = a;
            y = b;
        }
    }

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    //BufferedReader br = new BufferedReader(new FileReader("qual.in"));

    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);
    //PrintWriter pw = new PrintWriter("qual.out");

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public Main() throws FileNotFoundException {
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    long mod = Long.MAX_VALUE;

}