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.util.*;

public class D {

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        while (t --> 0) solver.solve(1, scan, out);
        out.close();
    }

    static class Task {

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            int n = scan.nextInt(), m = scan.nextInt();
            long[] a = new long[n];
            HashSet<Long> have = new HashSet<>();
            PriorityQueue<Item> curr = new PriorityQueue<>();
            for(int i = 0; i < n; i++) {
                a[i] = scan.nextLong();
                have.add(a[i]);
            }
            for(int i = 0; i < n; i++) {
                Item aa = getPos(a[i], 0, have);
                if(aa != null) {
                    curr.add(aa);
                    have.add(aa.pos);
                }
                Item bb = getNeg(a[i], 0, have);
                if(bb != null) {
                    curr.add(bb);
                    have.add(bb.pos);
                }
            }
            long total = 0;
            long[] ans = new long[m];
            for(int i = 0; i < m; i++) {
                Item p = curr.poll();
                total += p.dist;
                ans[i] = p.pos;
                Item aa = getPos(ans[i], p.dist, have);
                if(aa != null) {
                    curr.add(aa);
                    have.add(aa.pos);
                }
                Item bb = getNeg(ans[i], p.dist, have);
                if(bb != null) {
                    curr.add(bb);
                    have.add(bb.pos);
                }
            }
            out.println(total);
            for(long i : ans) out.print(i + " ");
        }

        static Item getPos(long curr, long add, HashSet<Long> have) {
            if(!have.contains(curr+1)) return new Item(add+1, curr+1);
            return null;
        }

        static Item getNeg(long curr, long add, HashSet<Long> have) {
            if(!have.contains(curr-1)) return new Item(add+1, curr-1);
            return null;
        }

        static class Item implements Comparable<Item> {
            long dist;
            long pos;

            public Item(long a, long b) {
                dist = a;
                pos = b;
            }
            @Override
            public int compareTo(Item o) {
                return Long.compare(dist, o.dist);
            }
        }
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}