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)

// import scala.io.StdIn._
import java.util.Scanner

object Main extends App {
  def readALine(c:Int):List[Int] = if (c > 0) sc.nextInt::readALine(c-1) else Nil
  def readLines(r:Int, c:Int):List[List[Int]] = if (r > 0) readALine(c)::readLines(r-1, c) else Nil
  val sc = new Scanner(System.in)
  val N = sc.nextInt
  val K = sc.nextLong
  val ls = readALine(N)
//  println(ls)

  def analyze():(Int, Int, Int) = {
    def search(x:Int):Option[(Int, Int)] = {
      def iter(y:Int, ac:Int):Int = if (y == x) ac else iter(ma(y), ac+1)

      // print(s"x:$x ")
      // println(used.mkString(","))
      if (usedTowns(x)) Some(iter(1, 0), iter(ma(x), 1)) else None
    }

    def iter(pos:Int):(Int, Int, Int) = {
      search(pos) match {
        case Some((l, r)) => (pos, l, r)
        case None => {
          usedTowns.update(pos, true)
          iter(ma(pos))
        }
      }
    }

    iter(1)
  }

  def move(s:Int, t:Int):Int = if (t == 0) s else move(ma(s), t-1)

  val ma = (0::ls).toArray
  val usedTowns = Array.fill(N+1)(false)
  val (pos, lead, loop) = analyze()

  // println(s"pos:$pos  load:$lead  loop:$loop")
  println(move(pos, ((K-lead) % loop).toInt))
}