B. Funny Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA sequence of n numbers is called permutation if it contains all numbers from 1 to n exactly once. For example, the sequences [3, 1, 4, 2], [1] and [2,1] are permutations, but [1,2,1], [0,1] and [1,3,4] are not.For a given number n you need to make a permutation p such that two requirements are satisfied at the same time:  For each element p_i, at least one of its neighbors has a value that differs from the value of p_i by one. That is, for each element p_i (1 \le i \le n), at least one of its neighboring elements (standing to the left or right of p_i) must be p_i + 1, or p_i - 1.  the permutation must have no fixed points. That is, for every i (1 \le i \le n), p_i \neq i must be satisfied. Let's call the permutation that satisfies these requirements funny.For example, let n = 4. Then [4, 3, 1, 2] is a funny permutation, since:   to the right of p_1=4 is p_2=p_1-1=4-1=3;  to the left of p_2=3 is p_1=p_2+1=3+1=4;  to the right of p_3=1 is p_4=p_3+1=1+1=2;  to the left of p_4=2 is p_3=p_4-1=2-1=1.  for all i is p_i \ne i. For a given positive integer n, output any funny permutation of length n, or output -1 if funny permutation of length n does not exist.InputThe first line of input data contains a single integer t (1 \le t \le 10^4) — the number of test cases.The description of the test cases follows.Each test case consists of f single line containing one integer n (2 \le n \le 2 \cdot 10^5).It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, print on a separate line:   any funny permutation p of length n;  or the number -1 if the permutation you are looking for does not exist. ExampleInput
543752Output
3 4 2 1
-1
6 7 4 5 3 2 1
5 4 1 2 3
2 1NoteThe first test case is explained in the problem statement.In the second test case, it is not possible to make the required permutation: permutations [1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 2, 1] have fixed points, and in [2, 3, 1] and [3, 1, 2] the first condition is met not for all positions.
543752
3 4 2 1 -1 6 7 4 5 3 2 1 5 4 1 2 3 2 1
['constructive algorithms', 'math', '*800']