Bob is organizing the annual tournament of gold. There are $n$ participants in a line, each starting with $0$ gold. Initially, the entire row of participants is "selected". A round of the tournament proceeds as follows:

1. Bob selects a random subarray of the currently "selected" part of the row. Each subarray has equal probability of being chosen, including the same currently "selected" part.
2. He gives $1$ gold to each participant in the subarray.
3. He sets this subarray as the new "selected" part of the row.

After $k$ rounds of the tournament proceed, what is the expected amount of gold of each participant ?

It can be proven that the expected amount of gold for the $i^{th}$ participant can be represented as a fraction  $\dfrac{P_i}{Q_i}$ with $Q_i \neq 0$ and $gcd(P_i,Q_i)=1$. Print $n$ space-separated integers, the $i^{th}$ of which is $P_i \cdot Q_i^{-1}$  modulo $998244353$

It can be proved that $Q^{-1}$ Modulo $998244353$ exists under the following constraints. 

Input Format:

The first and only line of input contains two space-separated integers, $n$ and $k$.

Output Format:

Print $n$ space separated integers, the $i^{th}$ integer denoting the answer for the $i^{th}$ participant .

Constraints:

$1 \le n,k \le 500$

Note that the Expected Output Feature for Custom Invocation is not supported for this contest.