Choosing Malatang Ingredients

Hayak likes putting several ingredients into malatang. Adding many ingredients does not always make it tastier, though. Each pair of ingredients has a compatibility score, so some combinations taste good together and others do not. Hayak is stuck on this problem.

How can Hayak maximize the flavor of malatang when using exactly $K$ ingredients?

Let $C_{i,j}$ be the compatibility of ingredient $i$ and ingredient $j$ when they are put in together. The flavor of the malatang is the sum of the compatibility scores over every pair of ingredients in the pot. If $G$ is the chosen group of ingredients, the flavor is:

$\sum_{i, j\in G,\ i < j}C_{i,j}$

For Hayak, find the maximum flavor when exactly $K$ ingredients are used.

The first line contains two integers $N$ ($1 \leq N \leq 10$) and $K$ ($1 \leq K \leq N$), separated by a space. The number of ingredients is $N$, and $K$ is the number of ingredients to choose.

The next $N$ lines describe the compatibility scores. Line $i+1$ contains the sequence $C_{i,1}, C_{i,2}, \ldots, C_{i,N}$ of integers, separated by spaces. ($-1000 \leq C_{i,j} \leq 1000$) It is given that $C_{i,i} = 0$ and $C_{i,j} = C_{j,i}$.

Print one line with the maximum flavor of malatang when exactly $K$ ingredients are used.