Problem Description
You are given a connected tree with N nodes and N-1 edges, rooted at node 0.
Rar the Cat wants you to answer Q queries regarding the tree. For each query, you will be provided with 2 integers, X and K. You are to output the Kth parent of the X node. In the event that node X does not have that many parent nodes, print -1 instead.
Limits
For all testcases, 0 ≤ A, B < N and 0 < X < N
Subtask 1 (23%): 1 ≤ N ≤ 1000, 1 ≤ Q ≤ 5000
Subtask 2 (28%): 1 ≤ N ≤ 100000, 1 ≤ Q ≤ 500000. However, each node can at most have 2 edges.
Subtask 3 (49%): 1 ≤ N ≤ 100000, 1 ≤ Q ≤ 500000.
Subtask 4 (0%): Sample Testcases.
Input
The first line of input will contain one integer, N.
The following N-1 lines will contain 2 integers each, A and B. This denotes that there is an edge between node A and node B.
As the resulting tree is guaranteed to be connected, do note that A will not be equal to B. Also, no two pairs of A and B will be the same.
The next line of input will contain Q, the number of queries.
The following Q lines will contain 2 integers each, X and K.
Output
You are to output Q lines of 1 integer each, one per query.
For each query, you are to output the Kth parent of node X. Print -1 instead of node X does not have K parents.
Sample Testcase 1
Input
10
0 1
1 2
2 3
3 4
4 5
6 0
7 2
2 8
3 9
5
5 3
5 5
7 2
6 2
8 2
Output
2
0
1
-1
1