Problem

A company has N employees numbered from 1 to N.

Employee 1 is the CEO.

For every employee i (2 ≤ i ≤ N), you are given their direct manager.

The hierarchy forms a rooted tree.

You have to answer Q independent queries.

Each query contains two integers:

X — an employee. K — number of levels to move upward.

Return the employee that is exactly K levels above X.

If such an employee does not exist, print -1.

Input

The first line contains

N Q

The second line contains N−1 integers

P2 P3 ... PN

where Pi is the direct manager of employee i.

Each of the next Q lines contains

X K Output

For every query print the answer on a new line.