Problem Statement

Among the elements of a permutation $P=(P_1,\ldots,P_N)$ of $(1,\ldots,N)$, those that satisfy the following condition are called good elements:

• The element can be included in both a longest increasing subsequence and a longest decreasing subsequence of $P$.

You are given integers $N$ and $K$. Determine whether there exists a permutation $P$ of $(1,\ldots,N)$ such that there are exactly $K$ good elements, and if it exists, find one.

Answer for $T$ test cases.

Constraints

• All input values are integers
• $1 \leq T \leq 2\times 10^5$
• $1 \leq N \leq 2\times 10^5$
• $0\leq K \leq N$
• The sum of $N$ over all test cases does not exceed $2\times 10^5$.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N K

Output

Output $T$ lines.

For the $i$-th line, if there does not exist a permutation satisfying the condition for the $i$-th test case, output -1. If it exists, output one of them in the following format:

P_1 \ldots P_N

If there are multiple solutions satisfying the condition, any of them will be accepted.