A14862 | Let's Play the Hat?

The Hat is a game of speedy explanation/guessing words (similar to Alias). It's fun. Try it! In this problem, we are talking about a variant of the game when the players are sitting at the table and everyone plays individually (i.e. not teams, but individual gamers play).

$n$ people gathered in a room with $m$ tables ( $n \ge 2m$ ). They want to play the Hat $k$ times. Thus, $k$ games will be played at each table. Each player will play in $k$ games.

To do this, they are distributed among the tables for each game. During each game, one player plays at exactly one table. A player can play at different tables.

Players want to have the most "fair" schedule of games. For this reason, they are looking for a schedule (table distribution for each game) such that:

- At any table in each game there are either $\lfloor\frac{n}{m}\rfloor$ people or $\lceil\frac{n}{m}\rceil$ people (that is, either $n/m$ rounded down, or $n/m$ rounded up). Different numbers of people can play different games at the same table.
- Let's calculate for each player the value $b_i$ — the number of times the $i$ -th player played at a table with $\lceil\frac{n}{m}\rceil$ persons ( $n/m$ rounded up). Any two values of $b_i$ must differ by no more than $1$ . In other words, for any two players $i$ and $j$ , it must be true $|b_i - b_j| \le 1$ .

For example, if $n=5$ , $m=2$ and $k=2$ , then at the request of the first item either two players or three players should play at each table. Consider the following schedules:

- First game: $1, 2, 3$ are played at the first table, and $4, 5$ at the second one. The second game: at the first table they play $5, 1$ , and at the second — $2, 3, 4$ . This schedule is not "fair" since $b_2=2$ (the second player played twice at a big table) and $b_5=0$ (the fifth player did not play at a big table).
- First game: $1, 2, 3$ are played at the first table, and $4, 5$ at the second one. The second game: at the first table they play $4, 5, 2$ , and at the second one — $1, 3$ . This schedule is "fair": $b=[1,2,1,1,1]$ (any two values of $b_i$ differ by no more than $1$ ).

Find any "fair" game schedule for $n$ people if they play on the $m$ tables of $k$ games.

The first line of the input contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the test.

Each test case consists of one line that contains three integers $n$ , $m$ and $k$ ( $2 \le n \le 2\cdot10^5$ , $1 \le m \le \lfloor\frac{n}{2}\rfloor$ , $1 \le k \le 10^5$ ) — the number of people, tables and games, respectively.

It is guaranteed that the sum of $nk$ ( $n$ multiplied by $k$ ) over all test cases does not exceed $2\cdot10^5$ .

For each test case print a required schedule — a sequence of $k$ blocks of $m$ lines. Each block corresponds to one game, a line in a block corresponds to one table. In each line print the number of players at the table and the indices of the players (numbers from $1$ to $n$ ) who should play at this table.

If there are several required schedules, then output any of them. We can show that a valid solution always exists.

You can output additional blank lines to separate responses to different sets of inputs.