Devu and Churu like to play with trees a lot. Today, they have a rooted unbalanced K-ary tree T consisting of N nodes and each node in the tree is labeled uniquely with the integers from 1 to N. Node with label 1 is the root of the tree T

To play with this tree, They have decided to perform Q operations on their tree T. In each operation, they shall be given a list of K nodes. Now, they need to find for all the nodes in this list, a node X, such that node X is an ancestor of all nodes in the given list, and the depth of node X is highest among all possible ancestors of the nodes in the list.

Please refer sample test case for better understanding of the problem.

Input:

The first line of the input contains 2 space separated integers N and Q denoting the number of nodes in the tree T and number of operations to be performed. Each of the next $N-1$ lines of input contains a single integer where the integer in the $i^{th}$ line is the parent of node with label $i+1$

Each of the next $2 \times Q$ lines of input contains Q operations where each operation spans over 2 lines and has following format :

• The first line of each operation contains an integer K denoting the number of nodes in the given operation.
• Second line of each operation contains K space separated integers denoting labels of nodes over which you need to perform given operation.

Output

For each of the Q operation, Print the required answer in a new line.

Constraints

• 1 ≤ N, Q ≤ 10⁵
• 1 ≤ K ≤ N
• sum of K over all operations does not exceed 10⁵
• Given nodes in any operation are labelled with integers from 1 to N