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)

{-# LANGUAGE BangPatterns #-}
import Data.Array.Unboxed
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import qualified Data.IntMap as M
readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
type Sym = Array Int Int
main = do
  [n,k] <- map read . words <$> getLine
  a <-  getIntList
  let a' = listArray (1,n) a
  print $ solve n k a' ! 1

dot :: Int -> Sym -> Sym -> Sym
dot n s t = listArray (1,n) $ map (\i ->s ! (t ! i)) [1..n]

solve :: Int -> Int -> Sym -> Sym
solve !n !k !s
  | k == 1 = s
  | odd k = s <> solve n (k-1) s
  | otherwise = t <> t
    where (<>) = dot n
          t = solve n (k `div` 2) s