Problem Description

You are given a set $S=\{1..n\}$. It guarantees that n is odd. You have to do the following operations until there is only $1$ element in the set:

Firstly, delete the smallest element of $S$. Then randomly delete another element from $S$.

For each $i \in [1,n]$, determine the probability of $i$ being left in the $S$.

It can be shown that the answers can be represented by $\frac{P}{Q}$, where $P$ and $Q$ are coprime integers, and print the value of $P \times Q^{-1} \space mod $ $\space 998244353.$

Input

The first line containing the only integer $T(T \in [1,40])$ denoting the number of test cases.

For each test case:

The first line contains a integer $n$ .

It guarantees that: $ \sum n \in [1,5 \times 10^6]$.

Output

For each test case, you should output $n$ integers, $i$-th of them means the probability of $i$ being left in the $S$.

1
3

0 499122177 499122177