Description

You have a sequence $\{p_n\}$ where initially $p_i = i(1 \leq i \leq n)$.

Each time you can choose $m$ distinct numbers $i_1, i_2\dots i_m$, and simultaneously set all of $p_{i_1}, p_{i_2}\dots p_{i_m}$ into their mean. Note that the mean may not be an integer. In this case, it will never be rounded.

You need to minimize the number of operations to make $p_1 = p_2 = \dots = p_n$.

Input Format

Each test consists of multiple test cases. The first line contains a single integer $T(1\leq T\leq 1.2\times 10^4)$ --- the number of sets of test cases. The description of each test case follows.

In each test case, the only line contains two integers --- $n$($1 \leq n \leq 2\times 10^5$) and $m$($1\le m\le n$), representing the length of the sequence and the number $m$.

It's guaranteed that the sum of $n$ over all testcases does not exceed $10^6$.

Output Format

For each test case, on the first line, output the minimum number of operations, $s$.

On the next $s$ lines, each line contains $m$ distinct integers in the range $[1, n]$ representing an operation.

If there's no solution, just print $s = -1$.

If there are multiple solutions, print any.

1
6 4

2
1 2 5 6
2 3 4 5

Hint

Sample #1

• $[1,2,3,4,5,6]\to [3.5,3.5,3,4,3.5,3.5]\to [3.5,3.5,3.5,3.5,3.5,3.5]$。
• There may be different but valid solutions.

Constraints

This problem uses subtasks.

Note that the full score of this problem in this contest is $50$. Your actually score is half of the subtask scores displayed below.

• Subtask 0 (20 pts): $1\leq \sum n\leq 10$.
• Subtask 1 (40 pts): $1\leq \sum n\leq 10^3$.
• Subtask 2 (40 pts): No Special Constraints.

It is guaranteed that $1 \leq T \leq 1.2\times 10^4$, $1 \leq m \leq n \leq 2\times 10^5$, $1 \leq \sum n \leq 10^6$.