18610번 - Yet Another Convolution 다국어

You are given an integer array \(a_1, \dots , a_n\) and \(a_n\) integer array \(b_1, \dots , b_n\).

You have to calculate the array \(c_1, \dots , c_n\) defined as follows:

\[c_k = \max_{gcd(i,j)=k}{|a_i - b_j|}\text{.}\]

The first line of input contains a single integer \(n\) (\(1 \le n \le 10^5\)).

The second line of input contains \(n\) integers \(a_1, \dots , a_n\) (\(1 \le a_i \le 10^9\)).

The third line of input contains \(n\) integers \(b_1, \dots , b_n\) (\(1 \le b_i \le 10^9\)).

Output \(n\) integers \(c_1, \dots , c_n\).