Description

You are given integers $n$, $m$, and $k$.

Your task is to construct $k$ tuples $(x_{i,1},x_{i,2},\dots,x_{i,m})$ of size $m$ that satisfy the conditions below:

• $x_{i,j}$ is an integer in $[1,n]$;
• For any two tuples, after removing an element from the same position in both tuples, the resulting tuples (which have size $m-1$) are not equal. In other words, there still exists at least one position at which the remaining elements differ.

Formally, you need to satisfy:

• $\forall 1\le i\le k,1\le j\le m,x_{i,j}\in [1,n] \cap \mathbb{Z^+}$;
• $\forall 1\le i<j\le k,1\le p\le m,\exists 1\le l\le m,l\neq p,x_{i,l}\neq x_{j,l}$.

Input Format

The first line contains three integers $n$, $m$, and $k$.

Output Format

Print $k$ lines. Each line should contain $m$ integers — the $j$-th integer in the $i$-th line represents $x_{i,j}$.

3 3 3

1 2 1
2 1 2
3 3 3

Hint

This problem involves a large output size, so I/O optimization is recommended.

The problem uses subtask dependencies: failing a prerequisite subtask will result in a score of zero for any subtask.

It is guaranteed that for all testcases, $1\le n\le 10^9,2\le m\le 10^5,1\le k \le n^{m-1},k\times m\le 10^6$。