P5850 calc Enhanced Version.

[Original problem link](https://www.luogu.com.cn/problem/P4463)

A sequence $a_1,\cdots,a_n$ is valid if and only if: - Its length is the given $n$. - $a_1,\cdots,a_n$ are all integers in $[1,k]$. - $a_1,\cdots,a_n$ are pairwise distinct. The value of a sequence is defined as the product of all numbers in it, i.e., $a_1\times a_2\times\cdots\times a_n$. Find the sum of the values of all different valid sequences. Two sequences are different if and only if they differ at any position. Output the answer modulo $998244353$.

One line with two numbers $k,m$.

There are $m$ lines in total. On the $i$-th line $(1\le i\le m)$, output the answer when $n=i$.

$\text{subtask 1 (84 pts)}$：$1\le m\le 500$. $\text{subtask 2 (16 pts)}$：$1\le m\le 5\times 10^5$，it is recommended to use an efficient output method. For all testdata, $1\le m\le k\le 998244352$. Translated by ChatGPT 5