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 java.util.Scanner

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

  def analyze():(Int, Int, Int) = {
    val usedTowns = Array.fill(N+1)(0)

    def iter(pos:Int, order:Int):(Int, Int, Int) = {
      if (usedTowns(pos) > 0) (pos, usedTowns(pos)-1, order - usedTowns(pos))
      else {
        usedTowns.update(pos, order)
        iter(ma(pos), order+1)
      }
    }

    iter(1, 1)
  }

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

  val ma = (0::ls).toArray
  val (pos, lead, loop) = analyze()

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