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.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Scanner;

public class Christmas_Tree {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int m = scn.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();
		}
		HashMap<Integer, Integer> map = new HashMap<>();

		LinkedList<Integer> queue = new LinkedList<>();
		for (int i = 0; i < n; i++) {
			map.put(arr[i], 0);
			queue.addLast(arr[i]);
		}
		long ans = 0;
		ArrayList<Integer> res = new ArrayList<>();
		while (queue.size() > 0) {
			if (res.size() == m) {
				break;
			}
			int val = queue.removeFirst();
			int adpre = val - 1;
			int adnt = val + 1;
			if (map.get(val) != 0) {
				ans += map.get(val);
				res.add(val);
			}
			if (!map.containsKey(adpre)) {
				map.put(adpre, map.get(val) + 1);
				queue.addLast(adpre);
			}
			if (!map.containsKey(adnt)) {
				map.put(adnt, map.get(val) + 1);
				queue.addLast(adnt);
			}
		}
		System.out.println(ans);
		for (int i : res) {
			System.out.print(i + " ");
		}
	}

}
