Permutation and GCD Set

### Read problems statements in [Russian](https://www.codechef.com/download/translated/COOK133/russian/PGCDS.pdf). We define the *GCD set* of an array $A$ of length $N$ as the set containing the GCD of all prefixes of $A$. More formally, the GCD set $G$ of $A$ contains the values $\gcd([A_1]), \gcd([A_1, A_2]), \gcd([A_1, A_2, A_3]), \ldots, \gcd([A_1, A_2, \ldots, A_n])$, where $\gcd(B)$ is the