Christmas Trees

题意翻译

有 $n$ 棵圣诞树和 $m$ 个人，第 $i$ 棵圣诞树所在的位置是 $a_i$ ，令 $d(x)$ 表示第 $x$ 个人到离他最近的圣诞树的距离，现在需要你给每个人安排一个位置，使得 $\sum\limits_{i=1}^m d(i)$ 最小，并输出这个值以及每个人的位置 注意任何位置最多只能有一个人或者圣诞树

题目描述

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, \dots, y_m $ be the positions of people (note that all values $ x_1, x_2, \dots, x_n, y_1, y_2, \dots, y_m $ should be distinct and all $ y_j $ should be integer). You want to find such an arrangement of people that the value $ \sum\limits_{j=1}^{m}\min\limits_{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\limits_{i=1}^{n} |y_j - x_i| $ ). Then you need to choose such positions $ y_1, y_2, \dots, y_m $ that $ \sum\limits_{j=1}^{m} d_j $ is the minimum possible.

输入输出格式

输入格式

The first line of the input contains two integers $ n $ and $ m $ ( $ 1 \le n, m \le 2 \cdot 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, \dots, x_n $ ( $ -10^9 \le x_i \le 10^9 $ ), where $ x_i $ is the position of the $ i $ -th Christmas tree. It is guaranteed that all $ x_i $ are distinct.

输出格式

In the first line print one integer $ res $ — the minimum possible value of $ \sum\limits_{j=1}^{m}\min\limits_{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, \dots, y_m $ ( $ -2 \cdot 10^9 \le y_j \le 2 \cdot 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, \dots, x_n, y_1, y_2, \dots, y_m $ should be distinct. If there are multiple answers, print any of them.

输入输出样例

输入样例 #1

2 6
1 5

输出样例 #1

8
-1 2 6 4 0 3 

输入样例 #2

3 5
0 3 1

输出样例 #2

7
5 -2 4 -1 2