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 Scala (2.13.1) (judge verdict: Runtime Error)

import java.util.Scanner

import scala.annotation.tailrec

object Main {
  def main(args: Array[String]): Unit = {
    //nextLineとnextを同時に使ったら死ぬ
    val sc = new Scanner(System.in)

    val n = sc.nextInt()
    val k = sc.nextLong()
    val as = Vector.fill(n)(sc.nextInt())

    var map = Vector.fill(n)(Vector())

    @scala.annotation.tailrec
    def dfs(now: Int,
            set: Set[Int] = Set.empty[Int],
            acc: Vector[Int] = Vector()): Vector[Int] = {
      if (set.contains(now)) acc :+ now
      else {
        dfs(as(now) - 1, set + now, acc :+ now)
      }
    }

    val m = dfs(0)
    val last = m.last
    val l = m.takeWhile(_ != last)
    val s = m.dropWhile(_ != last).init

    val ans = {
      if (k <= l.length) l(k.toInt) + 1
      else {
        if (l.isEmpty) {
          val mm = k % s.length
          val an = if (mm == s.length) 0 else mm
          s(an.toInt) + 1
        } else {
          val more = k - l.length + 1
          val mm = more % s.length

          val mmm =
            if (mm == 0) s.length else mm - 1

          s(mmm.toInt) + 1
        }
      }
    }

    println(ans)
  }

  //region

  def debug(args: Any*): Unit = {
    Console.err.println(args.mkString(" "))
  }

  def printExecTime(process: => Unit): Unit = {
    val start = System.currentTimeMillis
    process
    debug("処理時間： " + (System.currentTimeMillis - start) + " ミリ秒")
  }

  def bitSearch[T](n: Int, choice: Vector[T]): Vector[Vector[T]] = {
    @tailrec
    def bitSearchLogic(n: Int,
                       choice: Vector[T],
                       acc: Vector[Vector[T]]): Vector[Vector[T]] = {
      if (n == 0) acc
      else {
        val newAcc =
          acc.flatMap(vec => {
            choice.map(c => vec :+ c)
          })
        bitSearchLogic(n - 1, choice, newAcc)
      }
    }

    val firstAcc = choice.map(i => Vector(i))
    bitSearchLogic(n - 1, choice, firstAcc)
  }
  //endregion
}