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.