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: Wrong Answer)

{-# LANGUAGE BangPatterns #-}

import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as C
import Data.List
import Control.Monad
import Control.Arrow
--import Data.Foldable
--import Data.Char
import qualified Data.IntMap.Strict as IM
--import qualified Data.IntSet as IS
-- import Data.Sequence as Sq

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine




main = do
    [n,k] <- r'
    as <- r n
    reach <- U.thaw $ U.replicate n (-1 :: Int)
    (posS,hdS,repS) <- count as reach 0 0
    -- print (posS,hdS,repS)
    let rm =  (k - hdS) `mod` repS
    -- print rm 
    print $ succ $ trace as posS rm 


count as reach ac pos = do
    h <- UM.read reach pos
    if h == -1
        then do 
            UM.write reach pos ac
            count as reach (ac+1) (as U.! pos-1)
        else return (pos,h,ac-h)

trace as pos 0 = pos
trace as pos n = trace as (as U.! pos-1) (n-1)