Given an array $a$ of length $n$ and an array $b$ of length $m$, construct a grid of size $n \times m$, where the value in cell $(x,y)$ is denoted as $C[x,y]$ and calculated as $a_x + b_y$.

You start from $(1,1)$, and in each step, you choose a grid cell located at the bottom right to move to, until you reach $(n,m)$, aiming to maximize the sum of absolute differences between adjacent cells along the path.

Formally, your goal is to find a sequence $(x_1,y_1), (x_2,y_2), ..., (x_k,y_k)$ that satisfies the conditions

• $(x_1,y_1) = (1,1)$
• $(x_k,y_k) = (n,m)$
• $x_i \le x_{i+1},\ y_i \le y_{i+1},\ (x_i,y_i) \neq (x_{i+1},y_{i+1})\ \forall i\in [1, k)$

while maximizing the $\sum_{i=1}^{k-1} {|C[x_i,y_i]-C[x_{i+1},y_{i+1}]|}$.

4 4
1 3 3 1
8 10 8 5

4 2
5 7 8 10
10 3

11

12