194 Column of Eulerian Number

Given non-negative integer $k$ and positive integer $m$, find Eulerian numbers

$$ \left\langle 0\atop k\right\rangle,\left\langle 1\atop k\right\rangle,\dots ,\left\langle {m-1}\atop k\right\rangle $$

modulo $p=998244353$.

Where $\left\langle n\atop k\right\rangle =\sum_{j=0}^k(-1)^j\binom{n+1}{j}(k-j+1)^n$.

One line consists of integer $k,m$.

Print one line, containing $\left\langle 0\atop k\right\rangle \bmod{p},\left\langle 1\atop k\right\rangle \bmod{p},\dots ,\left\langle {m-1}\atop k\right\rangle \bmod{p}$.

$\left\langle n\atop 0\right\rangle =1,\forall n\geq 0$.

The problem contains $4$ subtasks. For the $n$-th subtask, we have $0\leq k\leq 10^{n+1},1\leq m\leq 10^{n+1}$.