E. 2..3...4.... Wonderful! Wonderful!time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputStack 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].InputEach 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.OutputFor 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.ExampleInput
434510Output
2 
4 
10 2 
487 162 85 10 
NoteIn 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]. 
434510
2  4  10 2  487 162 85 10  
['combinatorics', 'dp', 'math', '*2400']