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>) = ABC167D.main()

object ABC167D {
    fun log(message: Any?) {
        println(message)// TODO: ←消す
    }

    fun main() {
        val (N, K) = readLongs()
        val A = listOf(-1) + readInts() // 1-indexed

        val visited = mutableSetOf(1)
        val dests = mutableListOf(1)

        var next = A[dests.last()]
        while (!visited.contains(next)) {
            dests.add(next)
            visited.add(next)
            next = A[dests.last()]
        }
        val loopStart = dests.indexOf(next)
        val loopRange = dests.size - loopStart

        val destIndex = if (K <= dests.lastIndex) K
        else ((K - loopStart) % loopRange) + loopStart

        val ans = dests[destIndex.toInt()]
        println(ans)
    }


    /*####################################################################################*/

    fun readString() = readLine()!!
    fun readStrings() = readLine()!!.split(" ")
    fun readInt() = readLine()!!.toInt()
    fun readInts() = readLine()!!.split(" ").map { it.toInt() }
    fun readLong() = readLine()!!.toLong()
    fun readLongs() = readLine()!!.split(" ").map { it.toLong() }
    fun readMatrixRows(height: Int) = (1..height).map { readLine()!!.toList() }

    fun Boolean.yesOrNo() = if (this) "Yes" else "No"
    fun Double.toNaturalExpr() = println("%f".format(this))
}