BZOJ5119 CTT2017 Spanning Tree counting DP Division for FFT Stirling number __ Mathematics & Number Theory--the second kind of sterling

ctt= Tsinghua Training Topic

There are n n Dots, the right point for AI a_i, you want to connect a side, so that the picture into a tree.

For a d_i scheme T, the degree of the first I point is Di, and the value of the tree is:
Val (t) = (∏I=1NADIIDMI) (∑I=1NDMI) val (t) = (\prod_{i=1}^na_i^{d_i}d_i^m) (\sum_{i=1}^nd_i^m)
Find the value of all spanning trees and mod998244353 \bmod 998244353

n≤30000,m≤30 N\leq 30000,m\leq

It's easy to think of the prufer sequence

First take the child to simplify:
Ans= (∏I=1NADIIDMI) (∑I=1NDMI) =∑i=1ndmi (∏j=1nad