B. Interviews
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There are $$$x$$$ interviewers numbered from $$$1$$$ to $$$x$$$. Each of the interviewers can conduct at most $$$y$$$ interviews per day. An interview consists of $$$z$$$ different interviewers interviewing one participant.

Calculate the maximum number of participants that can be interviewed in a day (in other words, interviews that can be conducted in a day) and output any one of the schemes.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases.

For each test case:

  • The first line contains three integers $$$x$$$, $$$y$$$, and $$$z$$$ ($$$1 \le x, y, z \le 10$$$).
Output

For each test case,

  • In the first line output a single integer $$$k$$$  — the number of participants that can be interviewed in a day;
  • The next $$$k$$$ lines, for each line, output $$$z$$$ different space-separated integers, representing the numbers of the interviewers conducting the interviews;
  • The occurrence of each number should not exceed $$$y$$$.

If there are multiple schemes, you can output any.

Example
Input
3
3 1 2
3 2 2
4 10 5
Output
1
1 2
3
1 2
2 3
1 3
0