CF1930E.2..3...4.... Wonderful! Wonderful!

Stack has an array $a$ of length $n$ such that $a_i = i$ for all $i$ ( $1 \leq i \leq n$ ). He will select a positive integer $k$ ( $1 \leq k \leq \lfloor \frac{n-1}{2} \rfloor$ ) and do the following operation on $a$ any number (possibly $0$ ) of times.

• Select a subsequence $^\dagger$ $s$ of length $2 \cdot k + 1$ from $a$ . Now, he will delete the first $k$ elements of $s$ from $a$ . To keep things perfectly balanced (as all things should be), he will also delete the last $k$ elements of $s$ from $a$ .

Stack wonders how many arrays $a$ can he end up with for each $k$ ( $1 \leq k \leq \lfloor \frac{n-1}{2} \rfloor$ ). As Stack is weak at counting problems, he needs your help.

Since the number of arrays might be too large, please print it modulo $998\,244\,353$ .

$^\dagger$ A sequence $x$ is a subsequence of a sequence $y$ if $x$ can be obtained from $y$ by deleting several (possibly, zero or all) elements. For example, $[1, 3]$ , $[1, 2, 3]$ and $[2, 3]$ are subsequences of $[1, 2, 3]$ . On the other hand, $[3, 1]$ and $[2, 1, 3]$ are not subsequences of $[1, 2, 3]$ .

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 2 \cdot 10^3$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $3 \leq n \leq 10^6$ ) — the length of the array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ .

For each test, on a new line, print $\lfloor \frac{n-1}{2} \rfloor$ space-separated integers — the $i$ -th integer representing the number of arrays modulo $998\,244\,353$ that Stack can get if he selects $k=i$ .

In the first test case, two $a$ are possible for $k=1$ :

• $[1,2,3]$ ;
• $[2]$ .

In the second test case, four $a$ are possible for $k=1$ :

• $[1,2,3,4]$ ;
• $[1,3]$ ;
• $[2,3]$ ;
• $[2,4]$ .

In the third test case, two $a$ are possible for $k=2$ :

• $[1,2,3,4,5]$ ;
• $[3]$ .