Let $ n \ge 1$ and $ k \ge 3$ be integers. A circle is divided into $ n$ sectors $ a_1,a_2,\dots,a_n$. We will color the $ n$ sectors with $ k$ different colors such that $ a_i$ and $ a_{i + 1}$ have different color for each $ i = 1,2,\dots,n$ where $ a_{n + 1}=a_1$. Find the number of ways to do such coloring.