F. Let's Play the Hat?time limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe 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_imust 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.InputThe 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.OutputFor 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.ExampleInput
3
5 2 2
8 3 1
2 1 3
Output
3 1 2 3
2 4 5
3 4 5 2
2 1 3

2 6 2
3 3 5 1
3 4 7 8

2 2 1
2 2 1
2 2 1

3
5 2 2
8 3 1
2 1 3

3 1 2 3 2 4 5 3 4 5 2 2 1 3  2 6 2 3 3 5 1 3 4 7 8  2 2 1 2 2 1 2 2 1 
['brute force', 'constructive algorithms', 'greedy', 'math', '*2000']