Magical Coins

You are shopping in a store that has $n$ magical stones. For each stone, there is a probability $g$ that you will put it in your bag. The value $g$ is the same for all stones, all stones are independent, and you are given the value of $g$ modulo $998\ 244\ 353$. Suppose when you checkout, you have $r$ stones in your bag. Then you will be charged a price of $(ar+b)^k$ magical coins, where $a, b,