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)

import Control.Monad

import qualified Data.Set as S

inputIntList :: IO [Int]
inputIntList = map read . words <$> getLine :: IO[Int]

makeLoopList :: [Int] -> S.Set Int -> Int -> ([Int],[Int])
makeLoopList a st now = do
    if S.member now st
       then ([],[now])
       else do
           let to = a !! now
           let (before_loop, loop) = makeLoopList a (S.insert now st) to
           if (before_loop == [])
                then if (last loop) == now
                        then 
                            ([now], loop)
                        else 
                            ([], now:loop)
                else (now:before_loop, loop) 

    

main = do
    [n,k] <- inputIntList
    a <- inputIntList
    let (before_loop, loop) = makeLoopList (map (subtract 1) a) S.empty 0
    print $ if length before_loop >= k
               then before_loop !! (k-1)
               else loop !! ((k - (length before_loop)) `mod` (length loop)) + 1