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: Runtime Error)

fun main() {
    val l = readLine()!!.split(' ').map { it.toLong() }
    val a = readLine()!!.split(' ').map { it.toInt() }
    val visited: MutableList<Int> = mutableListOf(0)

    var loopStart = 0
    fun teleport(x: Int) {
        if (!visited.contains(x)) {
            visited.add(x)
            teleport(a[x]-1)
        } else {
            loopStart = visited.indexOf(x)
        }
    }
    teleport(a[0]-1)

    val res = if (l[1] < visited[loopStart]!!) {
        visited[l[1].toInt()]
    } else {
        visited[((l[1]-loopStart)%(visited.size-loopStart)+loopStart).toInt()]
    }
    println(res+1)
}