You are playing a game consisting of $n$ planets. Each planet has a teleporter to another planet (or the planet itself).

Your task is to process $q$ queries of the form: when you begin on planet $x$ and travel through $k$ teleporters, which planet will you reach?

Input

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

The second line has $n$ integers $t_1,t_2,\dots,t_n$: for each planet, the destination of the teleporter. It is possible that $t_i=i$.

Finally, there are $q$ lines describing the queries. Each line has two integers $x$ and $k$: you start on planet $x$ and travel through $k$ teleporters.

Output

Print the answer to each query.

Constraints

• $1 \le n, q \le 2 \cdot 10^5$
• $1 \le t_i \le n$
• $1 \le x \le n$
• $0 \le k \le 10^9$

Example

Input:

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

Output:

1
2
4