E. Treeland and Virusestime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThere are n cities in Treeland connected with n - 1 bidirectional roads in such that a way that any city is reachable from any other; in other words, the graph of cities and roads is a tree. Treeland is preparing for a seasonal virus epidemic, and currently, they are trying to evaluate different infection scenarios.In each scenario, several cities are initially infected with different virus species. Suppose that there are k_i virus species in the i-th scenario. Let us denote v_j the initial city for the virus j, and s_j the propagation speed of the virus j. The spread of the viruses happens in turns: first virus 1 spreads, followed by virus 2, and so on. After virus k_i spreads, the process starts again from virus 1.A spread turn of virus j proceeds as follows. For each city x not infected with any virus at the start of the turn, at the end of the turn it becomes infected with virus j if and only if there is such a city y that: city y was infected with virus j at the start of the turn; the path between cities x and y contains at most s_j edges; all cities on the path between cities x and y (excluding y) were uninfected with any virus at the start of the turn.Once a city is infected with a virus, it stays infected indefinitely and can not be infected with any other virus. The spread stops once all cities are infected.You need to process q independent scenarios. Each scenario is described by k_i virus species and m_i important cities. For each important city determine which the virus it will be infected by in the end.InputThe first line contains a single integer n (1 \leq n \leq 2 \cdot 10^5) — the number of cities in Treeland.The following n - 1 lines describe the roads. The i-th of these lines contains two integers x_i and y_i (1 \leq x_i, y_i \leq n) — indices of cities connecting by the i-th road. It is guaranteed that the given graph of cities and roads is a tree.The next line contains a single integer q (1 \leq q \leq 2 \cdot 10^5) — the number of infection scenarios. q scenario descriptions follow.The description of the i-th scenario starts with a line containing two integers k_i and m_i (1 \leq k_i, m_i \leq n) — the number of virus species and the number of important cities in this scenario respectively. It is guaranteed that \sum_{i = 1}^ q k_i and \sum_{i = 1}^ q m_i do not exceed 2 \cdot 10^5.The following k_i lines describe the virus species. The j-th of these lines contains two integers v_j and s_j (1 \leq v_j \leq n, 1 \leq s_j \leq 10^6) – the initial city and the propagation speed of the virus species j. It is guaranteed that the initial cities of all virus species within a scenario are distinct.The following line contains m_i distinct integers u_1, \ldots, u_{m_i} (1 \leq u_j \leq n) — indices of important cities.OutputPrint q lines. The i-th line should contain m_i integers — indices of virus species that cities u_1, \ldots, u_{m_i} are infected with at the end of the i-th scenario.ExampleInput
7
1 2
1 3
2 4
2 5
3 6
3 7
3
2 2
4 1
7 1
1 3
2 2
4 3
7 1
1 3
3 3
1 1
4 100
7 100
1 2 3
Output
1 2
1 1
1 1 1

7
1 2
1 3
2 4
2 5
3 6
3 7
3
2 2
4 1
7 1
1 3
2 2
4 3
7 1
1 3
3 3
1 1
4 100
7 100
1 2 3

1 2 1 1 1 1 1 
['data structures', 'dfs and similar', 'dp', 'shortest paths', 'trees', '*3000']