#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;
}

### Prompt

Develop a solution in cpp to the problem described below:

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

### Response

```cpp
#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;
}

```