description: 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 ≥ 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 ⌊n/m⌋ people or ⌈n/m⌉ 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 ⌈n/m⌉ 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| ≤ 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.
  
  Input
  
  The first line of the input contains an integer t (1 ≤ t ≤ 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 ≤ n ≤ 2⋅10^5, 1 ≤ m ≤ ⌊n/2⌋, 1 ≤ k ≤ 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⋅10^5.
  
  Output
  
  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.
  
  Example
  
  Input
  
  
  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
solution: #include <bits/stdc++.h>
  std::mt19937_64 gen(
      std::chrono::steady_clock::now().time_since_epoch().count());
  std::mt19937 gen1(std::chrono::steady_clock::now().time_since_epoch().count());
  long long int rng(long long int l, long long int r) {
    return std::uniform_int_distribution<long long int>(l, r)(gen);
  }
  const long double PI = atan(1.0) * 4;
  const int32_t INF32 = 2e9 + 7;
  const int64_t INF64 = 3e18;
  const int32_t LOG = 21;
  int32_t MOD = 1e9 + 7;
  using namespace std;
  void my_debugger(string second, long long int LINE_NUM) { cerr << '\n'; }
  template <typename start, typename... end>
  void my_debugger(string second, long long int LINE_NUM, start x, end... y) {
    if (second.back() != ',') {
      second += ',';
      cerr << "LINE(" << LINE_NUM << "): ";
    }
    long long int i = second.find(',');
    cerr << second.substr(0, i) << " = " << x;
    second = second.substr(i + 1);
    if (!second.empty()) cerr << ", ";
    my_debugger(second, LINE_NUM, y...);
  }
  void setMod(long long int mod_val) { MOD = mod_val; }
  void files_init() {
    freopen("file.in", "r", stdin);
    freopen("file.out", "w", stdout);
  }
  const long long int N = 1e6 + 5;
  const long long int LOGN = 20;
  void cyclic_shift(deque<long long int>& dq, long long int x) {
    for (long long int i = 0; i < (long long int)x; i++) {
      dq.push_front(dq.back());
      dq.pop_back();
    }
  }
  void print(const deque<long long int>& dq, const vector<long long int>& table,
             long long int m) {
    vector<vector<long long int>> vals(m + 1);
    for (long long int i = 0; i < (long long int)dq.size(); i++) {
      vals[table[i]].push_back(dq[i]);
    }
    for (long long int i = 1; i < (long long int)m + 1; i++) {
      cout << vals[i].size();
      for (auto it : vals[i]) cout << " " << it + 1;
      cout << '\n';
    }
  }
  int32_t main() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr);
    long long int tests = 1;
    cin >> tests;
    for (long long int ii = 0; ii < (long long int)tests; ii++) {
      long long int n, m, k;
      cin >> n >> m >> k;
      long long int rem = n % m;
      long long int start = (rem + rem * (n / m));
      long long int cur = 0;
      vector<long long int> table(n);
      long long int cur_table = 1;
      while (cur < start) {
        for (long long int i = 0; i < (long long int)(n / m) + 1; i++)
          table[cur + i] = cur_table;
        cur += (n / m) + 1;
        cur_table++;
      }
      while (cur < n) {
        for (long long int i = 0; i < (long long int)(n / m); i++)
          table[cur + i] = cur_table;
        cur += (n / m);
        cur_table++;
      }
      deque<long long int> dq;
      for (long long int i = 0; i < (long long int)n; i++) dq.push_back(i);
      long long int shift = start;
      for (long long int game = 0; game < (long long int)k; game++) {
        print(dq, table, m);
        cyclic_shift(dq, shift);
      }
      cout << '\n';
    }
    return 0;
  }
  