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) { new d(); }
	FS in = new FS();
	PrintWriter out = new PrintWriter(System.out);
	
	int n, m;
	long ans;
	int[] x, y;
	PriorityQueue<int[]> swp;
	
	d() {
		n = in.nextInt();
		m = in.nextInt();
		in.intArr(n, x = new int[n]);
		shuffle(x); Arrays.sort(x);
		int[] gap = new int[n - 1];
		for (int i = 0; i < n - 1; i++)
			gap[i] = x[i + 1] - x[i] - 1;

		swp = new PriorityQueue<>((a, b) -> a[2] == b[2] ? (a[1] == b[1] ? a[3] - b[3] : a[1] - b[1]) : a[2] - b[2]);
		if (n > 1) {
			for (int i = 0; i < n; i++) {
				if (i == 0) {
					swp.add(new int[]{m, -1, 0, i});
					if (gap[i] != 0) {
						int put = (gap[i] + 1) / 2;
						swp.add(new int[]{put, +1, 0, i});
						gap[i] -= put;
					}
				}
				else if (i == n - 1) {
					if (gap[i - 1] != 0)
						swp.add(new int[]{gap[i - 1], -1, 0, i});
					swp.add(new int[]{m, +1, 0, i});
				}
				else {
					if (gap[i - 1] != 0)
						swp.add(new int[]{gap[i - 1], -1, 0, i});
					if (gap[i] != 0) {
						int put = (gap[i] + 1) / 2;
						swp.add(new int[]{put, +1, 0, i});
						gap[i] -= put;
					}
				}
			}
		}
		else {
			swp.add(new int[]{m, -1, 0, 0});
			swp.add(new int[]{m, +1, 0, 0});
		}

		ans = 0;
		int ptr = 0;
		y = new int[m];
		while (ptr < m) {
			int[] use = swp.poll();
			use[2]++;
			y[ptr++] = x[use[3]] + use[1] * use[2];
			ans += (long) use[2];
			if (use[2] < use[0])
				swp.add(use);
		}

		out.println(ans);
		for (int pt : y) out.print(pt + " ");
		out.println();
		out.close();
	}

	void shuffle(int[] x) {
		int sz = x.length, j;
		Random r = new Random();
		for (int i = 0; i < sz; i++) {
			j = r.nextInt(i + 1);
			x[i] = x[j]^(x[i]^(x[j] = x[i]));
		}
	}
	
	int abs(int x) { if (x < 0) return -x; return x; }
	long abs(long x) { if (x < 0) return -x; return x; }
	int max(int x, int y) { if (x < y) return y; return x; }
	int min(int x, int y) { if (x > y) return y; return x; }
	long max(long x, long y) { if (x < y) return y; return x; }
	long min(long x, long y) { if (x > y) return y; return x; }

	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine()); }
				catch (Exception e) {}
			} return st.nextToken();
		}
		int nextInt() { return Integer.parseInt(next()); }
		long nextLong() { return Long.parseLong(next()); }
		double nextDouble() { return Double.parseDouble(next()); }

		void intArr(int sz, int[] x) { for (int i = 0; i < sz; i++) x[i] = nextInt(); }
		void longArr(int sz, long[] x) { for (int i = 0; i < sz; i++) x[i] = nextLong(); }
		void doubleArr(int sz, double[] x) { for (int i = 0; i < sz; i++) x[i] = nextDouble(); }
	}
}

