CF1283D.Christmas Trees

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.

一条无限长的数轴上有 $n$ 棵圣诞树。第 $i$ 棵树生长在位置 $x_i$ 处。所有 $x_i$ 互不相同。

每个整数点最多只能被一棵圣诞树、一个人占据，或完全空置；非整数点不能被任何东西占据。

有 $m$ 个人希望庆祝圣诞节。设 $y_1, y_2, \dots, y_m$ 表示这些人的位置（注意：所有值 $x_1, x_2, \dots, x_n, y_1, y_2, \dots, y_m$ 必须互不相同，且所有 $y_j$ 均为整数）。你需要找出一种人员位置安排方案，使得 $\sum\limits_{j=1}^{m}\min\limits_{i=1}^{n}|x_i - y_j|$ 达到最小可能值（即：所有人到其最近的圣诞树的距离之和最小）。

换言之，令 $d_j$ 表示第 $j$ 个人到其最近的圣诞树的距离（即 $d_j = \min\limits_{i=1}^{n} |y_j - x_i|$）。那么你需要选择位置 $y_1, y_2, \dots, y_m$，使得 $\sum\limits_{j=1}^{m} d_j$ 最小。

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.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 2 \cdot 10^5$）—— 分别表示圣诞树的数量和人数。

输入的第二行包含 $n$ 个整数 $x_1, x_2, \dots, x_n$（$-10^9 \le x_i \le 10^9$），其中 $x_i$ 表示第 $i$ 棵圣诞树的位置。保证所有 $x_i$ 互不相同。

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.

第一行输出一个整数 $res$ —— $\sum\limits_{j=1}^{m}\min\limits_{i=1}^{n}|x_i - y_j|$ 的最小可能值（即所有人到最近的圣诞树的距离之和）。

第二行输出 $m$ 个整数 $y_1, y_2, \dots, y_m$（满足 $-2 \cdot 10^9 \le y_j \le 2 \cdot 10^9$），其中 $y_j$ 表示第 $j$ 个人的位置。所有 $y_j$ 必须互不相同，且所有值 $x_1, x_2, \dots, x_n, y_1, y_2, \dots, y_m$ 也必须互不相同。

若存在多个答案，输出任意一个即可。