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: Accepted)

fun main(args: Array<String>) {
  val (tmp, k) = readLine()!!.split(" ").map { it.toLong() }
  val n = tmp.toInt()
  val a = readLine()!!.split(" ").map { it.toInt()-1 }.toIntArray()
  val count = LongArray(n) { -1L }
  var v = 0
  var c = 0L
  while (true) {
    if (count[v] >= 0) break
    count[v] = c
    v = a[v]
    c++
    if (c == k) {
      println(v+1)
      return
    }
  }
  val period = c-count[v]
  val rem = (k-count[v])%period
  for (i in count.indices) {
    if (count[i]-count[v] == rem) {
      println(i+1)
      return
    }
  }
}