Funny Permutation
Description
A 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.
The 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 $2 \cdot 10^5$.
For 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.
Input
The 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 $2 \cdot 10^5$.
Output
For 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.
5
4
3
7
5
2
3 4 2 1
-1
6 7 4 5 3 2 1
5 4 1 2 3
2 1
Note
The 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.