Planets Queries I

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