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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分