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: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N = in.next().toInt
  val K = in.next().toLong
  val A = new Array[Int](N+1)
  for (i <- 1 to N)
    A(i) = in.next().toInt

  //
  val dp = Array.fill[Int](N+1)(-1)
  var now = A(1)
  var cnt = 0
  var vol = -1
  breakable {
    while (true) {
      if (dp(now) == -1) {
        cnt += 1
        dp(now) = cnt
        now = A(now)
      }
      else {
        vol = dp(now) - 1
        break
      }
    }
  }


  if (K < cnt) {
    val k = K
    for (i <- 1 to N) {
      if (dp(i) == k)
        println(i)
    }
  }
  else {
    val m = (cnt-vol)
    var k = (K-cnt) % m
    if (k == 0) k = m
    for (i <- 1 to N) {
      if (dp(i) - vol == k)
        println(i)
    }
  }

}

object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.toList))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}