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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;

public class TaskD {
    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int n = in.nextInt();
        final int m = in.nextInt();
        final int[] x = in.readIntArr(n);
        Solution solution = new Solution(n, m, x);
        String[] res = solution.solution();
        out.printf("%s%n%s%n", res[0], res[1]);
        out.close();
        in.close();
    }

    private static class Solution {
        final int[] x;
        final int m, n;

        public Solution(final int n, final int m, final int[] x) {
            this.n = n;
            this.m = m;
            this.x = x;
        }

        public String[] solution() {
            Set<Long> visited = new HashSet<>();
            Queue<long[]> candidatesQ = new LinkedList<>();

            for (int i = 0; i < n; i++) {
                visited.add(x[i] + 0L);
                candidatesQ.add(new long[]{x[i] - 1, 1});
                candidatesQ.add(new long[]{x[i] + 1, 1});
            }

            int[] y = new int[m];
            long distance = 0;
            int yPos = 0;
            while (yPos < m) {
                long[] candidate = candidatesQ.poll();
                if (visited.contains(candidate[0])) {
                    continue;
                }
                distance += candidate[1];
                y[yPos++] = (int) candidate[0];
                visited.add(candidate[0]);
                candidatesQ.add(new long[]{candidate[0] + 1, candidate[1] + 1});
                candidatesQ.add(new long[]{candidate[0] - 1, candidate[1] + 1});
            }
            StringBuilder sB = new StringBuilder(2_000_000);
            for (int i = 0; i < m; i++) {
                sB.append(y[i]+" ");
            }
            return new String[]{distance + "", sB.toString()};
        }
    }

    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

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

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

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

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

    }

}