35485번 - Ahead Subarrays 서브태스크다국어

You are given two integer arrays $A$ and $B$, each of length $N$.

You want to select one contiguous subarray of length $K$ from each array to maximize the sum of the elements in the two chosen subarrays. However, the starting position of the subarray chosen from array $A$ must be strictly earlier than the starting position of the subarray from array $B$.

Formally, for integers $a$, $b$ satisfying $1 \le a < b \le N-K+1$ define

\[S(a, b) = \sum_{i = a}^{a + K - 1} A_i + \sum_{i = b}^{b + K - 1} B_i.\]

Your task is to find the maximum possible value of $S(a, b)$

The first line contains two integers $N$ and $K$, the length of the arrays and the length of each subarray. ($2 \le N \le 100\,000, 1 \le K \le N-1$)

The second line contains $N$ integers $A_1, A_2, \ldots, A_N$. ($-1\,000 \le A_i \le 1\,000$)

The third line contains $N$ integers $B_1, B_2, \ldots, B_N$. ($-1\,000 \le B_i \le 1\,000$)

Print a single integer: the maximum possible value of $S(a, b)$ under the given conditions.