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.

Definition of expected value modulo $998244353$

It can be proved that the sought expected values are always rational numbers. Additionally, under the constraints of this problem, when such a value is represented as an irreducible fraction $\\frac{P}{Q}$, it can be proved that $Q \\neq 0 \\pmod{998244353}$. Thus, there is a unique integer $R$ such that $R \\times Q = P \\pmod{998244353}$ and $0 \\le R < 998244353$. Print this $R$.

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.

Sample Input 1

3 3

Sample Output 1

499122182
37
748683574

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

Sample Input 2

7 8

Sample Output 2

449209977
705980975
631316005
119321168
62397541
596241562
584585746
378338599

Sample Input 3

2023 7

Sample Output 3

442614988
884066164
757979000
548628857
593993207
780067557
524115712