G. Shareefeh's Nar Fi Ard-El-Dyar
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Shareefeh just got married and moved in with Abu Shehab, when she walked into Ard-El-Dyar, she found out that Abu Shehab has no tree, she was mad and said how could you do this to the environment.

Se wants to help Abu Shehab improve his home's environment by planting a tree. She envisions a tree structure represented by a permutation $$$p$$$ of the integers from $$$1$$$ to $$$n$$$.

The tree is constructed as follows: for each $$$i$$$ from $$$2$$$ to $$$n$$$, there is an directed edge connecting $$$i$$$ to $$$\min(p_j : 1 \le j \lt i)$$$.

Shareefeh has specific requirements for this tree:

  • Depth: The depth of the tree (the maximum distance from the root to a leaf) must be exactly $$$d$$$.
  • Leaves: The tree must have exactly $$$k$$$ leaves, root can never be a leaf.
Input

The first line of input will contain one integer $$$T$$$, which is the number of test cases $$$(1 \leq T \leq 10^4)$$$.

For each test case

The only line of input will contain three integers $$$n$$$, $$$d$$$, and $$$k$$$ $$$(2 \leq n \leq 2 \cdot 10^5)$$$ $$$(1 \leq d, k \leq 2 \cdot 10^5)$$$ — denotes the length of the permutation, the depth of the tree, and the number of leaves.

It is guaranteed that the sum of $$$n$$$ across all test cases will not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print the permutation $$$p$$$ in a single line or print $$$-1$$$ denoting that such permutation does not exist.

Example
Input
2
5 3 2
5 3 1
Output
5 3 1 2 4
-1
Note