Let $k > 1, n > 2018$ be positive integers, and let $n$ be odd. The nonzero rational numbers $x_1,x_2,\ldots,x_n$ are not all equal and satisfy $$x_1+\frac{k}{x_2}=x_2+\frac{k}{x_3}=x_3+\frac{k}{x_4}=\ldots=x_{n-1}+\frac{k}{x_n}=x_n+\frac{k}{x_1}$$
Find:
a)	the product $x_1 x_2 \ldots x_n$ as a function of $k$ and $n$
b)	the least value of $k$, such that there exist $n,x_1,x_2,\ldots,x_n$ satisfying the given conditions.