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.