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 line has two integers $n$ and $q(1\le n,q\le 2\cdot 10^5)$: the number of planets and queries. The planets are numbered $1,2,\dots ,n$.

The second line has $n$ integers $t_1,t_2,\dots ,t_n(1\le t_i\le n)$: 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 $x(1\le x\le n)$ and $k(0\le k\le 10^9)$: you start on planet $x$ and travel through $k$ teleporters.

Output

Print the answer to each query.

Examples