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CSES Problem Set

Planets Queries I


Task | Statistics


CSES - Planets Queries ICSES - Planets Queries I

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
Example

Input:
4 3
2 1 1 4
1 2
3 4
4 1


Output:
1
2
4