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)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N = in.nextInt
  val K = in.nextLong
  val As = Array.fill(N)(in.nextInt - 1)
  val visited = Array.fill(N)(0)

  def teleport(pos: Int, step: Int): Int = {
    val next = As(pos)
    if (step == K) next
    else if (visited(next) == 0) {
      visited(next) = step + 1
      teleport(next, step + 1)
    } else {
      val diff = step + 1 - visited(next)
      val remain = (K - step) % diff
      def find(p: Int, r: Int): Int = if (r == 0) As(p) else find(As(p), r - 1)
      find(pos, remain.toInt)
    }
  }

  println(teleport(0, 1) + 1)
}