Company Queries I

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

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

Examples