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E. Military Problem
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In this problem you will have to help Berland army with organizing their command delivery system.

There are $$$n$$$ officers in Berland army. The first officer is the commander of the army, and he does not have any superiors. Every other officer has exactly one direct superior. If officer $$$a$$$ is the direct superior of officer $$$b$$$, then we also can say that officer $$$b$$$ is a direct subordinate of officer $$$a$$$.

Officer $$$x$$$ is considered to be a subordinate (direct or indirect) of officer $$$y$$$ if one of the following conditions holds:

  • officer $$$y$$$ is the direct superior of officer $$$x$$$;
  • the direct superior of officer $$$x$$$ is a subordinate of officer $$$y$$$.

For example, on the picture below the subordinates of the officer $$$3$$$ are: $$$5, 6, 7, 8, 9$$$.

The structure of Berland army is organized in such a way that every officer, except for the commander, is a subordinate of the commander of the army.

Formally, let's represent Berland army as a tree consisting of $$$n$$$ vertices, in which vertex $$$u$$$ corresponds to officer $$$u$$$. The parent of vertex $$$u$$$ corresponds to the direct superior of officer $$$u$$$. The root (which has index $$$1$$$) corresponds to the commander of the army.

Berland War Ministry has ordered you to give answers on $$$q$$$ queries, the $$$i$$$-th query is given as $$$(u_i, k_i)$$$, where $$$u_i$$$ is some officer, and $$$k_i$$$ is a positive integer.

To process the $$$i$$$-th query imagine how a command from $$$u_i$$$ spreads to the subordinates of $$$u_i$$$. Typical DFS (depth first search) algorithm is used here.

Suppose the current officer is $$$a$$$ and he spreads a command. Officer $$$a$$$ chooses $$$b$$$ — one of his direct subordinates (i.e. a child in the tree) who has not received this command yet. If there are many such direct subordinates, then $$$a$$$ chooses the one having minimal index. Officer $$$a$$$ gives a command to officer $$$b$$$. Afterwards, $$$b$$$ uses exactly the same algorithm to spread the command to its subtree. After $$$b$$$ finishes spreading the command, officer $$$a$$$ chooses the next direct subordinate again (using the same strategy). When officer $$$a$$$ cannot choose any direct subordinate who still hasn't received this command, officer $$$a$$$ finishes spreading the command.

Let's look at the following example:

If officer $$$1$$$ spreads a command, officers receive it in the following order: $$$[1, 2, 3, 5 ,6, 8, 7, 9, 4]$$$.

If officer $$$3$$$ spreads a command, officers receive it in the following order: $$$[3, 5, 6, 8, 7, 9]$$$.

If officer $$$7$$$ spreads a command, officers receive it in the following order: $$$[7, 9]$$$.

If officer $$$9$$$ spreads a command, officers receive it in the following order: $$$[9]$$$.

To answer the $$$i$$$-th query $$$(u_i, k_i)$$$, construct a sequence which describes the order in which officers will receive the command if the $$$u_i$$$-th officer spreads it. Return the $$$k_i$$$-th element of the constructed list or -1 if there are fewer than $$$k_i$$$ elements in it.

You should process queries independently. A query doesn't affect the following queries.

Input

The first line of the input contains two integers $$$n$$$ and $$$q$$$ ($$$2 \le n \le 2 \cdot 10^5, 1 \le q \le 2 \cdot 10^5$$$) — the number of officers in Berland army and the number of queries.

The second line of the input contains $$$n - 1$$$ integers $$$p_2, p_3, \dots, p_n$$$ ($$$1 \le p_i < i$$$), where $$$p_i$$$ is the index of the direct superior of the officer having the index $$$i$$$. The commander has index $$$1$$$ and doesn't have any superiors.

The next $$$q$$$ lines describe the queries. The $$$i$$$-th query is given as a pair ($$$u_i, k_i$$$) ($$$1 \le u_i, k_i \le n$$$), where $$$u_i$$$ is the index of the officer which starts spreading a command, and $$$k_i$$$ is the index of the required officer in the command spreading sequence.

Output

Print $$$q$$$ numbers, where the $$$i$$$-th number is the officer at the position $$$k_i$$$ in the list which describes the order in which officers will receive the command if it starts spreading from officer $$$u_i$$$. Print "-1" if the number of officers which receive the command is less than $$$k_i$$$.

You should process queries independently. They do not affect each other.

Example
Input
9 6
1 1 1 3 5 3 5 7
3 1
1 5
3 4
7 3
1 8
1 9
Output
3
6
8
-1
9
4