Binomial Fever

Chef loves dealing with binomial coefficients. Today, he came across an interesting problem, but he is currently busy in the kitchen. Can you help Chef solve this problem? You are given three positive integers $N$, $p$ and $r$. Calculate the sum $$S = \sum\limits_{i=0}^{N} \binom{p^i}{r} \,.$$ Since this sum could be very large, calculate it modulo $998,244,353$. ### Input - The first l