Dot Product (APCS 2022-06 Expert)

2.0s 256M

Given integer sequences \(A\) and \(B\), you may reverse either sequence. Choose a nonempty contiguous segment of equal length from each sequence. Its dot product is the sum of products of corresponding elements. Find the maximum possible dot product.

Input Format

The first line contains the sequence lengths \(n,m\). The second line contains the \(n\) elements of \(A\), and the third contains the \(m\) elements of \(B\).

Output Format

Print the maximum dot product. It may be negative; empty segments are forbidden.

Constraints

\(1\le n,m\le1000\), \(-100\le A_i,B_j\le100\).

Scoring

  • 20 points: \(n,m\le200\).
  • 80 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

5 5
-3 -3 3 3 -3
2 2 2 2 2

Sample Output 1

12

Sample Input 2

5 5
-3 -3 -3 5 -5
-5 5 -3 -3 -3

Sample Output 2

77

Sample Input 3

4 3
1 2 3 4
-1 -2 -3

Sample Output 3

-1

Source

APCS 2022-06 public archive version: i402。

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