Phone Call
TimeLimit:3000MS MemoryLimit:524288KB
64-bit integer IO format:%I64d
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Problem Description
There are $n$ houses in Bytetown, labeled by $1,2,...,n$. In each house, there is a person living here. Little Q lives in house $1$. There are $n-1$ bidirectional streets connecting these houses, forming a tree structure. In this problem, $S(u,v)$ denotes the house set containing all the houses on the shortest path from house $u$ to house $v$.
The Bytetown's phone line network consists of $m$ different lines. The $i$-th line can be expressed as $5$ integers $a_i,b_i,c_i,d_i,w_i$, which means for every two different houses $u$ and $v$ from set $S(a_i,b_i)\cup S(c_i,d_i)$, $u$ and $v$ can have a phone call costing $w_i$ dollars.
Picture from Wikimedia Commons
Little Q is now planning to hold a big party in his house, so he wants to make as many as possible people known. Everyone known the message can make several phone calls to others to spread the message, but nobody can leave his house.
Please write a program to figure out the maximum number of people that can join the party and the minimum total cost to reach that maximum number. Little Q should be counted in the answer.
The Bytetown's phone line network consists of $m$ different lines. The $i$-th line can be expressed as $5$ integers $a_i,b_i,c_i,d_i,w_i$, which means for every two different houses $u$ and $v$ from set $S(a_i,b_i)\cup S(c_i,d_i)$, $u$ and $v$ can have a phone call costing $w_i$ dollars.
Picture from Wikimedia Commons
Little Q is now planning to hold a big party in his house, so he wants to make as many as possible people known. Everyone known the message can make several phone calls to others to spread the message, but nobody can leave his house.
Please write a program to figure out the maximum number of people that can join the party and the minimum total cost to reach that maximum number. Little Q should be counted in the answer.
Input
The first line of the input contains an integer $T(1\leq T\leq15)$, denoting the number of test cases.
In each test case, there are $2$ integers $n,m(1\leq n,m\leq 100000)$ in the first line, denoting the number of houses and phone lines.
For the next $n-1$ lines, each line contains two integers $u$ and $v$, denoting a bidirectional edge between node $u$ and $v$.
For the next $m$ lines, each line contains $5$ integers $a_i,b_i,c_i,d_i,w_i(1\leq a_i,b_i,c_i,d_i\leq n,1\leq w_i\leq 10^9)$, denoting a phone line.
In each test case, there are $2$ integers $n,m(1\leq n,m\leq 100000)$ in the first line, denoting the number of houses and phone lines.
For the next $n-1$ lines, each line contains two integers $u$ and $v$, denoting a bidirectional edge between node $u$ and $v$.
For the next $m$ lines, each line contains $5$ integers $a_i,b_i,c_i,d_i,w_i(1\leq a_i,b_i,c_i,d_i\leq n,1\leq w_i\leq 10^9)$, denoting a phone line.
Output
For each test case, print a single line containing two integers, denoting the maximum number of people that can join the party and the minimum total cost to reach that maximum number.
SampleInput
1 5 2 1 2 1 3 2 4 2 5 1 3 2 4 100 2 2 4 2 10
SampleOutput
4 210 Hint Step 1 : 1 make a phone call to 2 using line 1, the cost is 100. Step 2 : 1 make a phone call to 3 using line 1, the cost is 100. Step 3 : 2 make a phone call to 4 using line 2, the cost is 10.