Score : $900$ points

Problem Statement

We have an $N$-sided die where all sides have the same probability to show up. Let us repeat rolling this die until every side has shown up.

For integers $i$ such that $1 \le i \le M$, find the expected value, modulo $998244353$, of the $i$-th power of the number of times we roll the die.

Constraints

• $1 \le N,M \le 2 \times 10^5$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$

Output

Print $M$ lines.

The $i$-th line should contain the expected value, modulo $998244353$, of the $i$-th power of the number of times we roll the die.

3 3

499122182
37
748683574

For $i=1$, you should find the expected value of the number of times we roll the die, which is $\frac{11}{2}$.

7 8

449209977
705980975
631316005
119321168
62397541
596241562
584585746
378338599

2023 7

442614988
884066164
757979000
548628857
593993207
780067557
524115712