SP1825 FTOUR2 - Free tour II

After the success of 2nd anniversary (take a look at problem **FTOUR** for more details), this 3rd year, Travel Agent SPOJ goes on with another discount tour. The tour will be held on _ICPC_ island, a miraculous one on the Pacific Ocean. We list **N** places (indexed from 1 to **N**) where the visitors can have a trip. Each road connecting them has an _interest value_, and this value can be _negative_ (if there is nothing interesting to view there). Simply, these **N** places along with the roads connecting them form a _tree structure_. We will choose _two places_ as the departure and destination of the tour. Since September is the festival season of local inhabitants, some places are extremely crowded (we call them _crowded places_). Therefore, the organizer of the excursion hopes the tour will visit _at most **K** crowded places_ (too tiring to visit many of them) and of course, the _total number of interesting value_ should be maximum. Briefly, you are given a map of **N** places, an integer **K**, and **M** id numbers of _crowded place_. Please help us to find the optimal tour. Note that we can visit each place only _once_ (or our customers easily feel bored), also the departure and destination places _don't need to be different_.

There is exactly one case. First one line, containing 3 integers **N K M**, with 1

Only one number, the maximum total interest value we can obtain.