102735: [AtCoder]ABC273 F - Hammer 2

Problem Statement

Takahashi is at the origin of a number line. Takahashi wants to reach the goal at coordinate $X$.

Also, there are $N$ walls and $N$ hammers on the number line.

• At coordinates $Y_1,Y_2,\dots,Y_N$ are walls of types $1,2,\dots,N$, respectively.
  • Initially, Takahashi cannot get over the walls.
• At coordinates $Z_1,Z_2,\dots,Z_N$ are hammers of types $1,2,\dots,N$, respectively.
  • When he arrives at a coordinate with a hammer, he obtains the hammer.
  • The hammer of type $i$ is dedicated to destroying the wall of type $i$. After he obtains the hammer of type $i$, he can destroy the wall of type $i$ and get over it.

Determine if he can reach the goal. If he can, find the minimum distance he travels.

Constraints

• All values in the input are integers.
• $1 \le N \le 1500$
• $1 \le |X|,|Y_i|,|Z_i| \le 10^9$
• The $(2 \times N + 1)$ coordinates $X,Y_i$ and $Z_i$ are distinct.

Input

The input is given from Standard Input in the following format:

$N$ $X$
$Y_1$ $Y_2$ $\dots$ $Y_N$
$Z_1$ $Z_2$ $\dots$ $Z_N$

Output

If Takahashi can reach the goal, print the minimum possible distance he travels as an integer.
Otherwise, print -1.

Sample Input 1

3 10
-2 8 -5
5 -10 3

Sample Output 1

40

Takahashi can reach the goal by traveling a distance of $40$ as follows, which is the minimum possible:

• He starts at coordinate $0$.
• He moves to coordinate $3$ to obtain the hammer of type $3$.
• He moves to coordinate $5$ to obtain the hammer of type $1$.
• He moves to coordinate $-2$ to destroy the wall of type $1$.
• He moves to coordinate $-5$ to destroy the wall of type $3$.
• He moves to coordinate $-10$ to obtain the hammer of type $2$.
• He moves to coordinate $8$ to destroy the wall of type $2$.
• He moves to coordinate $10$, which is the goal.

Sample Input 2

5 -1
10 -20 30 -40 50
-10 20 -30 40 -50

Sample Output 2

1

It may not be required that he obtains a hammer or destroys a wall to reach the goal.

Sample Input 3

1 100
30
60

Sample Output 3

-1

Takahashi cannot obtain the hammer of type $1$, and neither can he reach the goal.

Sample Input 4

4 865942261
703164879 -531670946 -874856231 -700164975
-941120316 599462305 -649785130 665402307

Sample Output 4

4078987507

问题描述

高桥在数轴的原点处。高桥想要到达坐标为$X$的目标。

数轴上还有$N$堵墙和$N$把锤子。

• 坐标为$Y_1,Y_2,\dots,Y_N$的地方分别有类型为$1,2,\dots,N$的墙。
  • 最初，高桥无法翻过这些墙。
• 坐标为$Z_1,Z_2,\dots,Z_N$的地方分别有类型为$1,2,\dots,N$的锤子。
  • 当他到达一个有锤子的坐标时，他会得到这个锤子。
  • 类型为$i$的锤子是专门用来摧毁类型为$i$的墙的。在他得到类型为$i$的锤子后，他可以摧毁类型为$i$的墙并翻过它。

确定他是否能够到达目标。如果他可以，找出他旅行的最短距离。

约束

• 输入中的所有值都是整数。
• $1 \le N \le 1500$
• $1 \le |X|,|Y_i|,|Z_i| \le 10^9$
• 坐标$X,Y_i$和$Z_i$的$(2 \times N + 1)$个值是不同的。

输入

输入将从标准输入中以以下格式给出：

$N$ $X$
$Y_1$ $Y_2$ $\dots$ $Y_N$
$Z_1$ $Z_2$ $\dots$ $Z_N$

输出

如果高桥可以到达目标，将他可能旅行的最短距离作为整数输出。
否则，输出-1。

样例输入1

3 10
-2 8 -5
5 -10 3

样例输出1

40

高桥可以通过以下方式旅行$40$的距离到达目标，这是可能的最短距离：

• 他从坐标$0$开始。
• 他移动到坐标$3$以获得类型为$3$的锤子。
• 他移动到坐标$5$以获得类型为$1$的锤子。
• 他移动到坐标$-2$以摧毁类型为$1$的墙。
• 他移动到坐标$-5$以摧毁类型为$3$的墙。
• 他移动到坐标$-10$以获得类型为$2$的锤子。
• 他移动到坐标$8$以摧毁类型为$2$的墙。
• 他移动到坐标$10$，即目标。

样例输入2

5 -1
10 -20 30 -40 50
-10 20 -30 40 -50

样例输出2

1

可能不需要他获得锤子或摧毁墙来到达目标。

样例输入3

1 100
30
60

样例输出3

-1

高桥无法获得类型为$1$的锤子，也无法到达目标。

样例输入4

4 865942261
703164879 -531670946 -874856231 -700164975
-941120316 599462305 -649785130 665402307

样例输出4

4078987507