Unique Sum 1

For any *zero-indexed* sequence $S$ of length $N$, define a function $G(S)$ as follows: $$ G(S) = \prod_{i=0}^{N-1} (S_i + i) $$ If $N = 0$, then $G(S) = 1$, i.e. the empty sequence has a value of $1$. --- You have an array $B$, which is initially empty. You are also given an array $A$ of length $N$, as well as a parameter $K$. For each $i$ from $1$ to $N$ in order, you must insert $A_i$ at