Sum vs MEX#13063
You're given an integer . A permutation of elements is called good if the following condition holds:
for each index (1 \le i \le n) : \sum\limits_{j=1}^{i} p_j is divisible by (p_1 , p_2 , \ldots, p_i).
where is the smallest positive integer which isn't present in the array maximize the permutation using some memorization-like process.
Find a good permutation of elements or report that it's impossible.
The first line contains a single integer (1 \le t \le 700)— the number of test cases.
The first line of each test case contains a single integer (1 \le n \le 2\cdot 10^5) — the length of the permutation.
It's guaranteed that the sum of over all testcases does not exceed 2 \cdot 10^5.
For each test case, print if there is a good permutation , then print a good permutation of elements , or print if there isn't any good permutation.
Example 1
In the third test case p = [3,1,4,2] works because
When i = 1 , p_1 = 3 , \text{MEX}(3) = 1 and 3 \bmod 1= 0 thus valid.
When i = 2 , p_1 + p_2 = 4 , \text{MEX}(3 , 1) = 2 and 4 \bmod 2=0 thus valid.
When i = 3 , p_1 + p_2 + p_3 = 8 , \text{MEX}(3 , 1 , 4) = 2 and 8 \bmod 2=0 thus valid.
When i = 4 , p_1 + p_2 + p_3 + p_4 = 10 , \text{MEX}(3,1,4,2) = 5 and 10 \bmod 5=0 thus valid.
Therefore the permutation is a valid construction.
Subtask ( points): \sum n \le 10.
Subtask ( points): No additional constraints.