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._

object Main extends App {
  val Array(n, k) = readLine.split(" ").map(_.toLong)
  val destinations = readLine.split(" ").map(_.toInt - 1) // 0 based index

  var v = 0
  var s = Array.empty[Int]
  val ord = Array.fill[Int](n.toInt)(-1)

  while (ord(v) == -1) {
    ord(v) = s.length
    s :+= v
    v = destinations(v)
  }
  val c = s.length - ord(v)
  val l = ord(v)

  val ans = if (k < l) s(l) else s(l + ((k - l) % c).toInt)
  println(ans + 1) // 1 based index
}