Starship Troopers

Time Limit: 5 Seconds
Memory Limit: 32768 KB

You, the leader of Starship Troopers, are sent to destroy a base of the bugs.
The base is built underground. It is actually a huge cavern, which consists
of many rooms connected with tunnels. Each room is occupied by some bugs, and
their brains hide in some of the rooms. Scientists have just developed a new
weapon and want to experiment it on some brains. Your task is to destroy the
whole base, and capture as many brains as possible.

To kill all the bugs is always easier than to capture their brains. A map is
drawn for you, with all the rooms marked by the amount of bugs inside, and the
possibility of containing a brain. The cavern's structure is like a tree in
such a way that there is one unique path leading to each room from the entrance.
To finish the battle as soon as possible, you do not want to wait for the troopers
to clear a room before advancing to the next one, instead you have to leave
some troopers at each room passed to fight all the bugs inside. The troopers
never re-enter a room where they have visited before.

A starship trooper can fight against 20 bugs. Since you do not have enough troopers,
you can only take some of the rooms and let the nerve gas do the rest of the
job. At the mean time, you should maximize the possibility of capturing a brain.
To simplify the problem, just maximize the sum of all the possibilities of containing
brains for the taken rooms. Making such a plan is a difficult job. You need
the help of a computer.

**Input**

The input contains several test cases. The first line of each test case contains
two integers N (0 < N <= 100) and M (0 <= M <= 100), which are the
number of rooms in the cavern and the number of starship troopers you have,
respectively. The following N lines give the description of the rooms. Each
line contains two non-negative integers -- the amount of bugs inside and the
possibility of containing a brain, respectively. The next N - 1 lines give the
description of tunnels. Each tunnel is described by two integers, which are
the indices of the two rooms it connects. Rooms are numbered from 1 and room
1 is the entrance to the cavern.

The last test case is followed by two -1's.

**Output**

For each test case, print on a single line the maximum sum of all the possibilities
of containing brains for the taken rooms.

**Sample Input**

5 10

50 10

40 10

40 20

65 30

70 30

1 2

1 3

2 4

2 5

1 1

20 7

-1 -1

Sample Output

50

7

Author:

**XU, Chuan**
Source:

**Zhejiang Provincial Programming Contest 2004**
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