UVALive 3902 Network （树+dfs）

Consider a tree network with n nodes where the internal nodes correspond to servers and the terminal
nodes correspond to clients. The nodes are numbered from 1 to n. Among the servers, there is an
original server S which provides VOD (Video On Demand) service. To ensure the quality of service for
the clients, the distance from each client to the VOD server S should not exceed a certain value k. The
distance from a node u to a node v in the tree is dened to be the number of edges on the path from u
to v. If there is a nonempty subset C of clients such that the distance from each u in C to S is greater
than k , then replicas of the VOD system have to be placed in some servers so that the distance from
each client to the nearest VOD server (the original VOD system or its replica) is k or less.
Given a tree network, a server S which has VOD system, and a positive integer k, nd the minimum
number of replicas necessary so that each client is within distance k from the nearest server which has
the original VOD system or its replica.
For example, consider the following tree network.

In the above tree, the set of clients is f1, 6, 7, 8, 9, 10, 11, 13g, the set of servers is f2, 3, 4, 5, 12,
14g, and the original VOD server is located at node 12.
For k = 2, the quality of service is not guaranteed with one VOD server at node 12 because the
clients in f6, 7, 8, 9, 10g are away from VOD server at distance > k. Therefore, we need one or more
replicas. When one replica is placed at node 4, the distance from each client to the nearest server of
f12, 4g is less than or equal to 2. The minimum number of the needed replicas is one for this example.
Input
Your program is to read the input from standard input. The input consists of T test cases. The number
of test cases (T) is given in the rst line of the input. The rst line of each test case contains an integer
n (3 n 1; 000) which is the number of nodes of the tree network. The next line contains two
integers s (1 s n) and k (k 1) where s is the VOD server and k is the distance value for ensuring
the quality of service. In the following n