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D. Christmas Trees

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Input

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.

Output

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.

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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