D. Christmas Treestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputIn 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.ExamplesInput
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 

2 6
1 5

8 -1 2 6 4 0 3  
['graphs', 'greedy', 'shortest paths', '*1800']