Description

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 $998244353$.

Input Format

One line with two numbers $k,m$.

Output Format

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

13 8

91
7462
546546
35387352
3869654
396558319
363789591
879373476

Hint

$\text{subtask 1 (84 pts)}$：$1\le m\le 500$.

$\text{subtask 2 (16 pts)}$：$1\le m\le 5\times 10^5$，it is recommended to use an efficient output method.

For all testdata, $1\le m\le k\le 998244352$.

Translated by ChatGPT 5