Nine Judges

There are $k$ problems proposed for the contest, and exactly $p$ of them must be chosen for the final problem set.

The problems have been evaluated by $n$ judges. Each judge has built their own preference list containing all the proposed problems, in order from the problem they like the most to the problem they like the least.

The XCPC finals are still far away, and nobody knows whether they will be held at all. The actual problem set is therefore chosen by an infinite procedure.

Initially, $t = 0$ and $S_0$ contains $p$ problems chosen uniformly at random from the $k$ proposed problems. Then the following actions are repeated indefinitely:

• Choose problems $i$ and $j$ uniformly at random such that $i \in S_t$ and $j \notin S_t$.
• If at least $(n+1)/2$ judges have put $j$ before $i$ in their preference list, let $S_{t+1} = S_t \setminus \{i\} \cup \{j\}$. Otherwise, let $S_{t+1} = S_t$.
• Increase $t$ by one.

A problem set $S$ is called plausible if there exists a positive probability threshold $\varepsilon$ such that there are infinitely many moments $t$ when the probability of $S_t = S$ is more than $\varepsilon$. In formal notation:

$S$ is plausible $\iff \exists \varepsilon > 0\ \forall T \ge 0\ \exists t \ge T: P(S_t = S) > \varepsilon$

The first line contains three integers $n$, $k$, and $p$ ($1 \le n \le 9$; $n$ is odd; $1 \le p < k \le 50\,000$), the number of judges, the number of proposed problems, and the number of problems to choose.

Each of the following $n$ lines contains $k$ integers $a_{i,1}, a_{i,2}, \ldots, a_{i,k}$ ($1 \le a_{i,j} \le k$, all values in a line are distinct). Here $a_{i,1}$ is the problem the $i$-th judge likes the most, $a_{i,2}$ is the second most liked, and so on.

Print $p$ distinct integers between 1 and $k$ in any order, denoting any plausible problem set.

In the example test case, some other possible answers are 1 2 5 and 2 4 5.