**Time limit:**1.00 s**Memory limit:**512 MB

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