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: Time Limit Exceeded)

import scala.collection.mutable
import scala.io.StdIn._

object Main extends App {
  val Array(n, k) = readLine.split(" ").map(_.toLong)
  val destinations = ("0 " + readLine).split(" ").map(_.toInt)

  var current = 0
  var jumps = 0
  var found = false
  var ans = 0

  val stepsToVisit = mutable.Map.empty[Int, Int]
  var visitedArr = Array.empty[Int]

  while (!found) {
    current = if (jumps == 0) 1 else destinations(current)

    if (jumps == k) {
      ans = current
      found = true
    } else if (stepsToVisit.contains(current)) {
      val stepsToFirstVisit = stepsToVisit(current)
      val loopLen = jumps - stepsToFirstVisit
      val shortcut = ((k - stepsToFirstVisit) % loopLen).toInt
      ans = visitedArr(stepsToFirstVisit + shortcut)
      found = true
    } else {
      stepsToVisit.put(current, jumps)
      visitedArr :+= current
      jumps += 1
    }
  }

  println(ans)
}