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:
- 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.
- He gives \(1\) gold to each participant in the subarray.
- 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.