Expected Cost

You are on a one-dimensional number line, initially at $x = 1$. You want to reach $x = N + 1$. You can do the following $2$ actions when you are at $x (x \le N)$: - Pay a cost of $A_x$ and move to $x + 1$. - Pay a cost of $B_x$ and move to a random position among the positions $x = 1, 2, \ldots, N + 1$. All of the $N + 1$ possibilities are equiprobable. Find the minimum expected cost to reach $