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] $ .