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?
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.
Print the answer to each query.
4 3 2 1 1 4 1 2 3 4 4 1· \n · · · \n · \n · \n · \n
1 2 4\n \n \n