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.PrintWriter;
// import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Set;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.LinkedList;

public class solve {
    public static void main(String[] args) throws IOException {
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final StringTokenizer st = new StringTokenizer(br.readLine());
        final int mTrees = Integer.parseInt(st.nextToken());
        final int nPeople = Integer.parseInt(st.nextToken());

        final StringTokenizer st2 = new StringTokenizer(br.readLine());
        int[] x = new int[mTrees];
        for (int i = 0; i < mTrees; i++) {
            x[i] = Integer.parseInt(st2.nextToken());
        }

        LinkedList<Integer> q = new LinkedList<>();
        LinkedList<Integer> dist = new LinkedList<>();
        Set<Integer> used = new HashSet<>();

        for (int i : x) {
            used.add(i);
        }

        for (int i : x) {
            if (!used.contains(i+1)) {
                q.add(i+1);
                used.add(i+1);
                dist.add(1);
            }
            if (!used.contains(i-1)) {
                q.add(i-1);
                used.add(i-1);
                dist.add(1);
            }
        }

        int[] ans = new int[nPeople];
        long totalDist = 0l;
        for (int i = 0; i < nPeople; i++) {
            int pos = q.remove();
            int d = dist.remove();
            totalDist += d;
            ans[i] = pos;
            if (!used.contains(pos+1)) {
                q.add(pos+1);
                used.add(pos+1);
                dist.add(d+1);
            }
            if (!used.contains(pos-1)) {
                q.add(pos-1);
                used.add(pos-1);
                dist.add(d+1);
            }
        }

        // PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        final StringBuilder sb = new StringBuilder();
        sb.append(totalDist).append('\n');
        for (int i : ans) {
            sb.append(i).append(' ');
        }
        System.out.printf("%s\n", sb);
        // out.close();
    }
}