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 (n, k) = readLine()!!.split(" ")
    val list = readLine()!!.split(" ").map(String::toInt)

    val pointList = mutableListOf(1, list[0])
    var index = list[0] - 1
    var diff = 0
    for (i in 0..n.toInt()) {
        val point = list[index]
        if (point == 1) {
            break
        }

        if (pointList.contains(point)) {
            val position = pointList.indexOfFirst { it == point }
            diff = pointList.size - position
            pointList.subList(0, position)
            break
        }

        pointList.add(point)
        index = point - 1
    }

    val last = ((k.toLong() - diff - 1) % pointList.size.toLong()).toInt()
    println(pointList[last])
}