Robotic Cow Herd

Bessie wants to fool Farmer John with a herd of $K$ convincing robotic cows ($1 \le K \le 100000$).

Building a robotic cow is harder than it sounds. A robot has $N$ ($1 \le N \le 100000$) locations that take a microcontroller, and exactly one microcontroller must be connected at each location. At location $i$ Bessie picks one of the models available there, and each model has its own cost.

The herd only looks convincing if no two robots behave the same way. No two robots may use exactly the same set of microcontrollers: for every pair of robots there must be at least one location where the two use a different microcontroller model. Two models offered at the same location count as different models even when they cost the same. The input always provides enough models to build $K$ different robots.

Bessie wants her herd as cheap as possible. Find the minimum total cost of building $K$ robots.

The first line contains $N$ and $K$ separated by a space.

Each of the next $N$ lines describes the models available at one location. Line $i$ starts with $M_i$ ($1 \le M_i \le 10$), the number of models available at location $i$, followed by $M_i$ space separated integers $P_{i,1}, \dots, P_{i,M_i}$, the costs of those models ($1 \le P_{i,j} \le 100000000$).

Print one line with the minimum total cost of building $K$ robots.