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: Wrong Answer)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(datN, datK) = readLine.split(" ").map(_.toLong)
    val datA = readLine.split(" ").map(_.toInt - 1)
    val sc = datA.map(a => (false, a))

    def detectLoopEnd(hop: Int, cur: Int, vec: Vector[(Boolean, Int)]): (Int, Int) = vec(cur) match {
        case (arrived, _) if(arrived && hop != 0) => (hop, cur)
        case (_, pos) => detectLoopEnd(hop + 1, pos, vec.updated(cur, (true, pos)))
    }
    val (hopLoopEnd, hopLoopPos) = detectLoopEnd(0, 0, sc.toVector.updated(0, (true, datA(0))))
    //println("DEBUG1:" + hopLoopEnd + " " + hopLoopPos)

    def detectLoopStart(hop: Int, cur: Int, dest: Int): Int = {
      if (cur == dest) hop
      else detectLoopStart(hop + 1, datA(cur), dest)
    }
    val hopLoopStart = detectLoopStart(0, 0, hopLoopPos)
    //println("DEBUG2:" + hopLoopStart)

    def traverse(pos: Int, count: Long): Int = {
      if(count == 0) pos
      else traverse(datA(pos), count - 1)
    }
    val ans = traverse(0, datK % (hopLoopEnd - hopLoopStart))
    println(ans + 1)
  }
}