CF1619F.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.

《帽子》是一款快速描述/猜词游戏（类似于“阿利斯”）。它很有趣，快去试试吧！在本题中，我们讨论的是该游戏的一种变体：玩家围坐在桌旁，各自独立进行游戏（即不组队，而是每位玩家单独参与）。

共有 $n$ 人聚集在一间屋内，屋中有 $m$ 张桌子（满足 $n \ge 2m$）。他们希望共进行 $k$ 轮《帽子》游戏。因此，每张桌子上将进行 $k$ 局游戏，且每位玩家恰好参与 $k$ 局游戏。

为此，需为每局游戏分别安排玩家到各张桌子的分配方案。在每一局游戏中，每位玩家恰好坐在一张桌子上（即每局每人只在一张桌子上游戏），但同一玩家可在不同局中坐在不同的桌子上。

玩家们希望制定尽可能“公平”的游戏日程表。因此，他们寻求一种日程安排（即每局游戏对应的桌子分配方案），使得：

• 在每一局游戏中，每张桌子上的人数要么是 $\lfloor\frac{n}{m}\rfloor$，要么是 $\lceil\frac{n}{m}\rceil$（即 $n/m$ 向下取整或向上取整）。同一张桌子在不同局中可容纳不同数量的玩家。
• 对每位玩家 $i$，定义 $b_i$ 为其在人数为 $\lceil\frac{n}{m}\rceil$（即 $n/m$ 向上取整）的桌子上的游戏局数。任意两个 $b_i$ 的值之差至多为 $1$。换言之，对任意两位玩家 $i$ 和 $j$，必须满足 $|b_i - b_j| \le 1$。

例如，当 $n=5$、$m=2$、$k=2$ 时，根据第一条要求，每张桌子在每局游戏中应有 $2$ 人或 $3$ 人。考虑如下两种安排：

• 第一局：玩家 $1, 2, 3$ 在第一张桌子，玩家 $4, 5$ 在第二张桌子；第二局：玩家 $5, 1$ 在第一张桌子，玩家 $2, 3, 4$ 在第二张桌子。该安排不公平，因为 $b_2 = 2$（第 $2$ 位玩家在“大桌”（即 $3$ 人桌）上玩了 $2$ 次），而 $b_5 = 0$（第 $5$ 位玩家从未在“大桌”上游戏）。
• 第一局：玩家 $1, 2, 3$ 在第一张桌子，玩家 $4, 5$ 在第二张桌子；第二局：玩家 $4, 5, 2$ 在第一张桌子，玩家 $1, 3$ 在第二张桌子。该安排公平：$b = [1,2,1,1,1]$（任意两个 $b_i$ 值之差均不超过 $1$）。

请为 $n$ 位玩家、$m$ 张桌子、共进行 $k$ 局游戏的情形，构造出任意一个“公平”的游戏日程表。

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 $2\cdot10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

每个测试用例由一行组成，该行包含三个整数 $n$、$m$ 和 $k$（$2 \le n \le 2\cdot10^5$，$1 \le m \le \lfloor\frac{n}{2}\rfloor$，$1 \le k \le 10^5$）—— 分别表示人数、桌子数和游戏数。

保证所有测试用例中 $nk$（即 $n$ 与 $k$ 的乘积）的总和不超过 $2\cdot10^5$。

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.

对每个测试用例，输出一个所需的赛程安排——即由 $k$ 个块组成的序列，每个块包含 $m$ 行。每个块对应一场比赛，块中的一行对应一张桌子。在每一行中，首先输出该桌子上的玩家人数，然后输出应在此桌子进行比赛的玩家编号（编号范围为 $1$ 到 $n$）。

若存在多个满足要求的赛程安排，则输出任意一个即可。可以证明，合法解一定存在。

你可以在不同输入组的输出之间添加额外的空行以作分隔。