\begin{aligned} &n,\ m\le 10^5\\ &a_i,\ b_i\le 10^9\\ &如何求下式的 n 次项系数（模998244353的值）\\ &\prod_{j=1}^{m}( \sum_{i=0}^{n} \frac{ \binom{b_j}{i+1} x^i}{(i+1)!} )^{a_j} \end{aligned}