A13357 | Tourism

Masha lives in a country with $n$ cities numbered from $1$ to $n$ . She lives in the city number $1$ .

There is a direct train route between each pair of distinct cities $i$ and $j$ , where $i \neq j$ . In total there are $n(n-1)$ distinct routes. Every route has a cost, cost for route from $i$ to $j$ may be different from the cost of route from $j$ to $i$ .

Masha wants to start her journey in city $1$ , take exactly $k$ routes from one city to another and as a result return to the city $1$ . Masha is really careful with money, so she wants the journey to be as cheap as possible. To do so Masha doesn't mind visiting a city multiple times or even taking the same route multiple times.

Masha doesn't want her journey to have odd cycles. Formally, if you can select visited by Masha city $v$ , take odd number of routes used by Masha in her journey and return to the city $v$ , such journey is considered unsuccessful.

Help Masha to find the cheapest (with minimal total cost of all taken routes) successful journey.

First line of input had two integer numbers $n,k$ ( $2 \leq n \leq 80; 2 \leq k \leq 10$ ): number of cities in the country and number of routes in Masha's journey. It is guaranteed that $k$ is even.

Next $n$ lines hold route descriptions: $j$ -th number in $i$ -th line represents the cost of route from $i$ to $j$ if $i \neq j$ , and is 0 otherwise (there are no routes $i \to i$ ). All route costs are integers from $0$ to $10^8$ .

Output a single integer — total cost of the cheapest Masha's successful journey.