Problem:
Score: 400 points

Problem Statement

The Kingdom of Takahashi has N towns, numbered 1 through N.

There is one teleporter in each town. The teleporter in Town i (1 \leq i \leq N) sends you to Town A_i.

Takahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Help the king by writing a program that answers this question.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

1 \leq K \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Sample Input 1

4 5
3 2 4 1

Sample Output 1

4

If we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \to 3 \to 4 \to 1 \to 3 \to 4.

Sample Input 2

6 727202214173249351
6 5 2 5 3 2

Sample Output 2

2

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import qualified Data.Map as M
import Data.Maybe
type Sym a = M.Map a a

main = do
  [n,k] <- map read . words <$> getLine
  a <- map read . words <$> getLine
  let a' = zip [0..n] (map (\t -> t-1) a)
  print $ 1 + (Data.Maybe.fromMaybe 0 $ M.lookup 0 $ solve k (M.fromList a') )

(.^) :: (Ord a) => a -> Sym a -> a
x .^ g = Data.Maybe.fromMaybe x (M.lookup x g) -- if x `notElem` supp (P g), then x is not moved

dot ::(Ord a) => Sym a -> Sym a -> Sym a
dot sigma tau = M.fromList [(x,x .^ sigma .^ tau) | x <- M.keys (sigma `M.union` tau)]

solve :: Int -> Sym Int-> Sym Int
solve k sigma
  | k == 1 = sigma
  | even k = s `dot` s
  | otherwise  = sigma `dot` solve (k-1) sigma
    where s = solve (k `div` 2) sigma