X-Men

There is a kingdom called Dream Kingdom with $N$ cities connected by $N - 1$ roads. There is a path between any two city. The length of each road is one kilometer. The cities are numbered from $1$ to $N$. There are $M$ X-men in this kingdom. The $i$-th X-man is in the city numbered $a_i(1 \leq a_i \leq N)$. There can be no or multiple X-men in one city.

Everyone start to walk simultaneously. At the beginning of each hour, one man will choose a adjacent city ("adjacent" means there is a road between two cities) which is on the shortest path to the city where there is a man he can communicate with now. If there are several eligible adjacent cities that can be chosen, the X-man will choose one of them \textbf{randomly}. Each x-man will make the decision and move simultaneously. The speed of X-men is only one kilometer per hour. So they will move to chosen city at the end of each hour. X-men can communicate with the people whose distance to him is \textbf{more than one} kilometer at this time. If there are no X-man he can communicate with now, he will not move in the following hour.

The king of the Dream Kingdom want to arrest X-men. And at the beginning of one hour he could check whether there is any X-man can move in the following hour. If the king knows no X-man can move in the following hour, he will send the army to catch all X-men immediately.

Now the king wants you to help him calculate the expected hours he could arrest the X-men. In other words, you need to calculate the expected hours such that all X-men stop moving.

The first line is the number of test cases.

For each test case, the first line contains two positive numbers $N(1 \leq N \leq 10^3), M(1 \leq M \leq 10^3)$. The second line contains $M$ numbers $a_i (1 \leq a_i \leq N)$.

The following $N - 1$ lines describe the roads. Each line contains two integers $u, v$ $(1 \leq u,v \leq N)$, denoting there is a road between city $u$ and city $v$.

For each test case, output one number in one single line representing the answer. You should output your answer rounded to two decimal places.

2
7 3
5 6 7
1 2
1 3
1 4
5 2
6 3
4 7
3 3
1 1 2
1 2
2 3

2.00
0.00

2017 ACM/ICPC 哈尔滨赛区网络赛——测试专用

In the first example, each X-man only have one adjacent city can be chosen to move in the first hour. They will move from city {5, 6, 7} to city {2, 3, 4} respectively. Each X-man only have one adjacent city can be chosen to move in the second hour, too. They will all move to city {1}. And then all of them can't feel any X-man such that distance between two X-men is more than one unit length. So they will be arrested immediately after two hours from the beginning to now. This is the only situation. So the answer is {2/1 = 2.00}.