F. Tree Queriestime limit per test6 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given a tree consisting of n vertices. Recall that a tree is an undirected connected acyclic graph. The given tree is rooted at the vertex 1.You have to process q queries. In each query, you are given a vertex of the tree v and an integer k.To process a query, you may delete any vertices from the tree in any order, except for the root and the vertex v. When a vertex is deleted, its children become the children of its parent. You have to process a query in such a way that maximizes the value of c(v) - m \cdot k (where c(v) is the resulting number of children of the vertex v, and m is the number of vertices you have deleted). Print the maximum possible value you can obtain.The queries are independent: the changes you make to the tree while processing a query don't affect the tree in other queries.InputThe first line contains one integer n (1 \le n \le 2 \cdot 10^5) — the number of vertices in the tree.Then n-1 lines follow, the i-th of them contains two integers x_i and y_i (1 \le x_i, y_i \le n; x_i \ne y_i) — the endpoints of the i-th edge. These edges form a tree.The next line contains one integer q (1 \le q \le 2 \cdot 10^5) — the number of queries.Then q lines follow, the j-th of them contains two integers v_j and k_j (1 \le v_j \le n; 0 \le k_j \le 2 \cdot 10^5) — the parameters of the j-th query.OutputFor each query, print one integer — the maximum value of c(v) - m \cdot k you can achieve.ExampleInput
8
6 7
3 2
8 3
5 7
7 4
7 1
7 3
6
1 0
1 2
1 3
7 1
5 0
7 200000
Output
5
2
1
4
0
4
NoteThe tree in the first example is shown in the following picture:  Answers to the queries are obtained as follows:  v=1,k=0: you can delete vertices 7 and 3, so the vertex 1 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 2 \cdot 0 = 5;  v=1,k=2: you can delete the vertex 7, so the vertex 1 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 1 \cdot 2 = 2.  v=1,k=3: you shouldn't delete any vertices, so the vertex 1 has only one child (vertex 7), and the score is 1 - 0 \cdot 3 = 1;  v=7,k=1: you can delete the vertex 3, so the vertex 7 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 1 \cdot 1 = 4;  v=5,k=0: no matter what you do, the vertex 5 will have no children, so the score is 0;  v=7,k=200000: you shouldn't delete any vertices, so the vertex 7 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 0 \cdot 200000 = 4. 
8
6 7
3 2
8 3
5 7
7 4
7 1
7 3
6
1 0
1 2
1 3
7 1
5 0
7 200000

5 2 1 4 0 4 
['brute force', 'dp', 'trees', '*2800']