think-cell Round 1 |
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Finished |
Stack has an array a of length n such that ai=i for all i (1≤i≤n). He will select a positive integer k (1≤k≤⌊n−12⌋) and do the following operation on a any number (possibly 0) of times.
Stack wonders how many arrays a can he end up with for each k (1≤k≤⌊n−12⌋). As Stack is weak at counting problems, he needs your help.
Since the number of arrays might be too large, please print it modulo 998244353.
† 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≤t≤2⋅103) — 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≤n≤106) — the length of the array a.
It is guaranteed that the sum of n over all test cases does not exceed 106.
For each test, on a new line, print ⌊n−12⌋ space-separated integers — the i-th integer representing the number of arrays modulo 998244353 that Stack can get if he selects k=i.
434510
2 4 10 2 487 162 85 10
In the first test case, two a are possible for k=1:
In the second test case, four a are possible for k=1:
In the third test case, two a are possible for k=2:
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