Yet Another Convolution

You are given an integer array $a_1, \dots, a_n$ and an integer array $b_1, \dots, b_n$ of length $n$. Compute the array $c_1, \dots, c_n$ defined as follows:

$c_k = \max_{\gcd(i,j)=k} |a_i - b_j|$

The first line contains a single integer $n$ ($1 \le n \le 10^5$). The second line contains $n$ integers $a_1, \dots, a_n$ ($1 \le a_i \le 10^9$). The third line contains $n$ integers $b_1, \dots, b_n$ ($1 \le b_i \le 10^9$).

Output $n$ integers $c_1, \dots, c_n$.