Stack has a positive integer P(P > 1).
He starts a game where his initial score is 0.

In the i^{th} turn, with a probability of $\frac{1}{2}, Stack adds \frac{1}{P^{i-1}}$ to his score.

Stack stops after N turns.

Let S_{i} be his score after i turns and F(i) denote the [expected value] of S_{i}^{2}.

For each integer i(1 ≤ i ≤ N), find the value of F(i) modulo 998244353.

------ Input Format ------

The only line of input contains two space-separated positive integers N and P, as mentioned in the statement.

------ Output Format ------

Print N space-separated integers. For each integer i(1 ≤ i ≤ N), output the value of F(i) modulo 998244353.

Formally, let M=998244353. It can be shown that the answer can be expressed as an irreducible fraction $\frac{x}{y}$, where x and y are integers and $y \not$ $\equiv 0 \pmod{M}$.
Output the integer equal to $x \cdot y^{-1} \bmod M$ .
In other words, output such an integer z that 0 ≤ z < M and $z \cdot y \equiv x \pmod{M}$.
.

------ Constraints ------

$1 ≤ N ≤ 3 \cdot 10^{5}$
$2 ≤ P ≤ 10^{5}$

----- Sample Input 1 ------
2 2

----- Sample Output 1 ------
499122177 124780545

----- explanation 1 ------
$S_{1}$ can be $0$ or $1$ with equal probability.
Thus $F(1)=\frac{0 \cdot 0}{2}+\frac{1 \cdot 1}{2} = \frac{1}{2}$.

$F(2)=\frac{7}{8}$.

----- Sample Input 2 ------
10 343

----- Sample Output 2 ------
499122177 379526990 822885144 761122022 256959043 151932103 340445396 758502677 478338987 125853909

----- explanation 2 ------

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