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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import kotlin.math.*
import java.util.*

data class Visit(var seq: Int = 0, var visited: Boolean = false)

fun main(args: Array<String>) {
  val (_n, _k) = readLine()!!.split(' ')
  val n = _n.toInt()
  val k = _k.toLong()
  val a = readLine()!!.split(' ').map(String::toInt)

  val v = Array(n) { Visit() }
  val r = mutableListOf<Int>()
  var cur = 1
  var seq = 0
  while (!v[cur - 1].visited) {
    val visit = v[cur - 1]
    visit.seq = seq++
    visit.visited = true
    r += cur
    cur = a[cur - 1]
  }
  val p = v[cur - 1]
  val len = r.size - p.seq
  println(r[p.seq + ((k - p.seq) % len).toInt()])
}