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 nk = readLine()!!.split(" ").map { it.toLong() }
    val n = nk[0].toInt()
    val k = nk[1]
    val a = readLine()!!.split(" ").map { it.toInt() }
    var count:Long = 0
    val flagList = List(n){ 0 }.toMutableList()
    val countFlag = MutableList(n){ 0 }
    countFlag[0] = a[0]
    flagList[0] = 1

    fun mytereport(y: Int) {
        count++
        if (flagList[a[y] - 1] != 0){
            val mae = flagList[a[y] - 1]
            count -= mae
            count += 1
            return
        } else {
            flagList[a[y] - 1] = count.toInt() + 1
            countFlag[count.toInt()] = a[y]
            mytereport(a[y] - 1)
        }
    }
    mytereport(0)

    val x = k % count
    println(countFlag[x.toInt()])
}