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? \InputFile 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. \OutputFile Print the answer to each query.