P3868 [TJOI2009] Guess the Number

There are two groups of numbers, each with $k$ elements. The numbers in the first group are denoted by $a_1,a_2,\cdots ,a_k$, and the numbers in the second group are denoted by $b_1,b_2,\cdots ,b_k$. The numbers in the second group are pairwise coprime. Find the smallest $n\in \mathbb{N}$ such that for $\forall i\in [1,k]$, $b_i | (n-a_i)$ holds.

The first line contains an integer $k$. The second line contains $k$ integers: $a_1,a_2,\cdots ,a_k$. The third line contains $k$ integers: $b_1,b_2,\cdots ,b_k$.

Output a single integer, which is the required answer $n$.

Constraints: $1\le k \le 10$，$|a_i|\le 10^9$，$1\le b_i\le 6\times 10^3$，$\prod_{i=1}^k b_i\le 10^{18}$. Time limit per test case: 1 second. Note: For ```C/C++``` language, 64-bit integers should be declared as ```long long```. If using ```scanf``` and ```printf``` (as well as ```fscanf```, ```fprintf```, etc.), use the ```%lld``` specifier. Translated by ChatGPT 5