A company has $n$ employees, who form a tree hierarchy where each employee has a boss, except for the general director.

Your task is to process $q$ queries of the form: who is employee $x$'s boss $k$ levels higher up in the hierarchy?

Input

The first input line has two integers $n$ and $q$: the number of employees and queries. The employees are numbered $1,2,\dots,n$, and employee $1$ is the general director.

The next line has $n-1$ integers $e_2,e_3,\dots,e_n$: for each employee $2,3,\dots,n$ their boss.

Finally, there are $q$ lines describing the queries. Each line has two integers $x$ and $k$: who is employee $x$'s boss $k$ levels higher up?

Output

Print the answer for each query. If such a boss does not exist, print $-1$.

Constraints

• $1 \le n,q \le 2 \cdot 10^5$
• $1 \le e_i \le i-1$
• $1 \le x \le n$
• $1 \le k \le n$

Example

Input:

5 3
1 1 3 3
4 1
4 2
4 3

Output:

3
1
-1