B. Special Permutation
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

A permutation of length $$$n$$$ is an array $$$p=[p_1,p_2,\dots, p_n]$$$ which contains every integer from $$$1$$$ to $$$n$$$ (inclusive) exactly once. For example, $$$p=[4, 2, 6, 5, 3, 1]$$$ is a permutation of length $$$6$$$.

You are given three integers $$$n$$$, $$$a$$$ and $$$b$$$, where $$$n$$$ is an even number. Print any permutation of length $$$n$$$ that the minimum among all its elements of the left half equals $$$a$$$ and the maximum among all its elements of the right half equals $$$b$$$. Print -1 if no such permutation exists.

Input

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$), the number of test cases in the test. The following $$$t$$$ lines contain test case descriptions.

Each test case description contains three integers $$$n$$$, $$$a$$$, $$$b$$$ ($$$2 \le n \le 100$$$; $$$1 \le a,b \le n$$$; $$$a \ne b$$$), where $$$n$$$ is an even number (i.e. $$$n \bmod 2 = 0$$$).

Output

For each test case, print a single line containing any suitable permutation. Print -1 no such permutation exists. If there are multiple answers, print any of them.

Example
Input
7
6 2 5
6 1 3
6 4 3
4 2 4
10 5 3
2 1 2
2 2 1
Output
4 2 6 5 3 1
-1
6 4 5 1 3 2 
3 2 4 1 
-1
1 2 
2 1