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: Accepted)

import Data.IntMap hiding (map, empty, insert, member)
import Data.IntSet hiding (map, fromList)
import Data.List hiding (insert)
import Data.Maybe

main :: IO ()
main = do
  l1 <- getLine
  l2 <- getLine
  let [n, k] = map read $ words l1 :: [Integer]
      a = fromList $ zip [1..] $ map read $ words l2 :: IntMap Int
      (lroute, loop_start) = g a empty [] 1
      loop_count = fromIntegral $ length lroute
      k' = if k > loop_count then (k - loop_start) `mod` (loop_count - loop_start) else k
      start = if k > loop_count then lroute !! (fromInteger loop_start) else 1
  -- print (loop_start, loop_count, k', start)
  print $ f a k' start

f as 0 x = x
f as 1 x = as ! x
f as k x = f as (k - 1) (as ! x)

g as visited route x = if x `member` visited then (reverse route, fromIntegral $ fromJust $ elemIndex x $ reverse route) else g as (insert x visited) (x:route) next
  where
    next = as ! x