Problem F
Fair Forgery

The 2025 Pokemon Association Presidential Elections have just concluded! There were $N$ candidates running for the position of president, and $M$ votes were received. Each vote $i$ is a ranking of the $N$ candidates, which is a permutation $p_{i,1}, p_{i,2}, \dots , p_{i,N}$ of the integers from $1$ to $N$, with $p_{i, 1}$ ranked the highest, followed by $p_{i, 2}$, and so on, until the lowest ranked $p_{i, N}$.

Selina is in charge of tallying the votes. However, when she checked the list of voters, she realised that there were supposed to be $K$ voters, not $M$ voters! In other words, some voters may have submitted more than one vote, some may have not voted, or some non-voters may have somehow cast their vote. Selina does not want to redo the election due to suspicions in legitimacy of the votes, so she decided to forge $K$ votes to replace the $M$ votes received. However, the $K$ votes should not be too suspicious.

After some deliberation, she decided that if the $K$ votes satisfy the following condition, then they are probably not too suspicious:

For all integers $1 \leq t \leq K$, $1 \leq l \leq N$, if a candidate appears in the highest $l$ ranks in at least $\left\lceil \frac{t \cdot M}{K} \right\rceil $ of the $M$ received votes, then he/she should appear in the highest $l$ ranks in at least $t$ of the $K$ forged votes.

Selina proved non-constructively that she can always forge $K$ such votes regardless of the $M$ votes she receives. However, she does not know how to actually forge these $K$ votes. Please help Selina with her forgery!

Input

The first line of the input contains 3 integers $N, M, K$ ($1 \leq M \leq 10^4$, $1 \leq N, K \leq 100$, $M \neq K$).

The next $M$ lines of the input each contain $N$ integers $p_{i, 1}, p_{i, 2}, \dots , p_{i, N}$, which is a permutation of $1$ to $N$.

Output

Output $K$ lines, where the $i^{\text{th}}$ line ($1 \leq i \leq K$) contains $N$ integers $q_{i, 1}, q_{i, 2}, \dots , q_{i, N}$ forming a permutation of $1$ to $N$, denoting the $i^{\text{th}}$ forged vote.

The $K$ votes should satisfy the condition mentioned.

Sample Explanation

For the first sample, we can verify that the provided sample output satisfies the conditions. An example of an output that does not satisfy the conditions is:

1 2 4 5 3

1 2 5 3 4

This is because we may take $t = 1, l = 3$ in the condition: in the $l = 3$ highest ranks in the given $M$ votes, candidate 3 appears $2 \geq \left\lceil \frac{t \cdot M}{K} \right\rceil = \left\lceil \frac{1 \cdot 4}{2} \right\rceil = 2$ times, so it should appear at least $t = 1$ times in the 3 highest ranks in the output $K$ votes. However, it appears 0 times in the $3$ highest ranks in the output $K$ votes.

5 4 2
1 2 3 4 5 
1 4 2 3 5 
1 2 3 4 5 
2 5 1 3 4 

1 2 3 4 5 
2 1 3 4 5 

10 2 4
1 4 5 2 7 6 10 9 3 8 
5 6 1 8 7 3 4 9 10 2 

1 4 5 2 7 6 10 9 3 8 
1 4 5 2 7 6 10 9 3 8 
5 6 1 8 7 3 4 9 10 2 
5 6 1 8 7 3 4 9 10 2