Score : $200$ points
There are $N$ balls in the $xy$-plane. The coordinates of the $i$-th of them is $(x_i, i)$. Thus, we have one ball on each of the $N$ lines $y = 1$, $y = 2$, $...$, $y = N$.
In order to collect these balls, Snuke prepared $2N$ robots, $N$ of type A and $N$ of type B. Then, he placed the $i$-th type-A robot at coordinates $(0, i)$, and the $i$-th type-B robot at coordinates $(K, i)$. Thus, now we have one type-A robot and one type-B robot on each of the $N$ lines $y = 1$, $y = 2$, $...$, $y = N$.
When activated, each type of robot will operate as follows.
When a type-A robot is activated at coordinates $(0, a)$, it will move to the position of the ball on the line $y = a$, collect the ball, move back to its original position $(0, a)$ and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
When a type-B robot is activated at coordinates $(K, b)$, it will move to the position of the ball on the line $y = b$, collect the ball, move back to its original position $(K, b)$ and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the $2N$ robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Input is given from Standard Input in the following format:
$N$ $K$ $x_1$ $x_2$ $...$ $x_N$
Print the minimum possible total distance covered by robots.
1 10 2
4
There are just one ball, one type-A robot and one type-B robot.
If the type-A robot is used to collect the ball, the distance from the robot to the ball is $2$, and the distance from the ball to the original position of the robot is also $2$, for a total distance of $4$.
Similarly, if the type-B robot is used, the total distance covered will be $16$.
Thus, the total distance covered will be minimized when the type-A robot is used. The output should be $4$.
2 9 3 6
12
The total distance covered will be minimized when the first ball is collected by the type-A robot, and the second ball by the type-B robot.
5 20 11 12 9 17 12
74