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문제

Byteland is an island with a number of cities connected by two-way roads. Road network is designed in such a way, that there is exactly one possibility to drive between any pair of cities (without turning back).

Unfortunately, hard times have come - Byteland is preparing for a war. The Lead Strategiest of Byteland is preparing a plan of defence of Byteland, which takes into account creation of a special security zone. The zone will be created by blocking some of the existing roads in Byteland in such a way, that it won't be possible to drive through these roads. In order to make the zone completely secure, following rules have to be fulfilled:

  • from each city inside the zone it has to be possible to drive to any other city inside that zone,
  • it is not possible to get from a city outside of the zone to the city inside the zone,
  • zone has to consist of exactly k cities.

Many different solutions to the problem are being considered - for different values of k, it is required to determine how many roads have to be blocked at minimum, to obtain a special security zone of size k (consisting of exactly k cities). Help the Lead Strategiest of Byteland - write a program which for specified value of k calculates required number of barricades.

Write a program which:

  • reads from the standard input description of the roads in Byteland and the set of queries (different k values),
  • for each query program should determine the minimal possible number of barricades that are sufficient to construct a special security zone of required size,
  • writes result to the standard output.

입력

The first line of the standard input contains one integer n (1 ≤ n ≤ 3 000), representing the number of cities in Byteland. Cities are numbered with numbers 1, 2, ..., n.

Each of the following n - 1 lines of the standard input contains pair of integers a, b (1 ≤ a, bn) separated with single space. Pair a, b represents a direct road connecting cities a and b. Each pair of cities is connected with at most one direct road.

In the following line of the standard input there is an integer m (1 ≤ mn) - it is the number of queries to process. Each of the following m lines contains one integer ki (ki ∈ {1, 2, 3, ..., n}). It represents query number i - the number of cities that have to be inside i'th special security zone.

출력

Your program should write to the standard output exactly m numbers, each of them in a separate line. The number in i'th line should be:

  • -1, if creation of a special security zone of size ki is not possible,
  • the minimal number of roads that have to be blocked in order to construct a special security zone of size ki otherwise.

예제 입력 1

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

예제 출력 1

2
1