Chiaki was trapped in a strange place which can be regarded as a connected undirected graph with n vertices (numbered from 1 to n) and m weighted edges (numbered from 1 to m). In the beginning, Chiaki is at vertex 1 with speed v equals to 1 unit per second and would like to go to the vertex n.
There are some special vertices in the graph, called \textit{acceleration vertex}. Once Chiaki reached an acceleration vertex, her speed will be doubled: from v to 2v. The same acceleration vertex can be used multiple times to achieve multiple acceleration, but it only works under this limitation: the last acceleration vertex Chiaki visited should not equal to the current acceleration vertex Chiaki reached.
For example, vertex 2 and 3 are acceleration vertices while 1, 4 and 5 are not. If Chiaki chooses the path , Chiaki's speed would be accelerated for three times (8 unit per second in the end). But if the path is , Chiaki would have only one acceleration.
Chiaki would like to know the minimum time needed to reach the vertex n.

输入描述:

There are multiple test cases. The first line of the input contains an integer T, indicating the number of test cases. For each test case:
The first line contains three integers n, m and k (2 ≤ n ≤ 100, 1 ≤ m ≤ 8000, 0 ≤ k ≤ n) -- the number of vertices, the number of edges and the number of special vertices.
Each of the following m lines contains three integers ui, vi and wi (1 ≤ ui, vi ≤ n, 1 ≤ wi ≤ 1000) denoting an edge with wi unit length connecting ui and vi.
The next line contains k integers p1,p2,...,pk (1 ≤ pi ≤ n) denoting the index of each \textit{acceleration vertex}.
It's guaranteed that the sum of n over all test cases will not exceed 1000 and the sum of m over all test cases will not exceed 80000.

输出描述:

For each test case, output a real number t denoting the minimum time to reach the vertex n and an integer s denoting the maximum times of acceleration Chiaki can achieve among all optimal solutions.
Your answer for t will be considered correct if and only if the absolute error or relative error of your answer is less than 10-8. And by the way, if s is greater than 32767, output ``Burst!'' (without the quotes) instead.

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

0.5000000000 2
2.0000000000 Burst!
3.5000000000 2