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 Data.Maybe
import Data.List
import qualified Data.ByteString.Char8 as BS

readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

teleport xs i = xs !! i

teleport_list xs ys i 0 = i : []
teleport_list xs ys i n | index == Nothing = teleport_list xs ys' (teleport xs i - 1) (n - 1)
                        | otherwise = ys'
                        where
                          index = elemIndex i ys
                          ys' = ys ++ [i] 

main = do
  [n_g, k_g] <- getIntList
  xs_g <- getIntList
  let xs = map fromIntegral xs_g
  let n = fromIntegral n_g
  let k = fromIntegral k_g
  let teleport_n = teleport_list xs [] 0 n
  let loop_start = fromJust (elemIndex (last teleport_n) teleport_n)
  let loop_end = length teleport_n - 2
  let modulation = loop_end - loop_start + 1
  if k < loop_start then
    putStrLn $ show (teleport_n !! k + 1)
  else do
    let teleport_count = k - loop_start
    let teleport_index = loop_start + teleport_count `mod` modulation
    putStrLn $ show (teleport_n !! teleport_index + 1)