Background

JXCSP-S T2

Problem Description

Given two sequences $a_i, b_i$ indexed from $1$ to $n$, define the function $S(l, r)$ $(1 \le l \le r \le n)$ as:

Please compute the value of the following expression:

Since the answer may be very large, you only need to output the result modulo $10^9 + 7$.

Input Format

The first line contains a positive integer $n$ indicating the length of the sequences.
The second line contains $n$ positive integers representing $a_i$.
The third line contains $n$ positive integers representing $b_i$.

Output Format

Output a single integer, the result modulo $10^9 + 7$.

3
2 3 4
3 4 5

244

5
11 22 33 44 55
12 34 56 78 90

201542

Hint

Constraints
For $20\%$ of the testdata: $n \le 10$, $a_i, b_i \le 10$.
For $40\%$ of the testdata: $n \le 200$, $a_i, b_i \le 100$.
For $70\%$ of the testdata: $n \le 3000$, $a_i, b_i \le 10^5$.
For $100\%$ of the testdata: $3 \le n \le 5 \times 10^5$, $1 \le a_i, b_i \le 10^9$.

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