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)

//package abc167.D

import java.io.*
import java.math.*
import java.util.*
import kotlin.math.*

var reader: BufferedReader = System.`in`.bufferedReader()
var writer: PrintWriter = PrintWriter(System.`out`)

fun next() = reader.readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextStrings() = next().split(" ")
fun nextInts() = nextStrings().map { it.toInt() }
fun nextLongs() = nextStrings().map { it.toLong() }
fun nextDoubles() = nextStrings().map { it.toDouble() }

fun put(v: Any?) = writer.print(v)
fun puts() = writer.println()
fun puts(v: Any?) = writer.println(v)

var debug = false
fun dp(v: Any?) {
    if (debug) println(v)
}
fun dp() {
    if (debug) println()
}

fun test(case: Int, input: String, expected: String) {
    reader = input.trimIndent().reader().buffered()

    val stringWriter = StringWriter()
    writer = PrintWriter(stringWriter)

    solve()
    writer.flush()

    val actual = stringWriter.toString()

    println("[test $case]")
    if ("${expected}" == actual) {
        println("OK")
    } else {
        println("NG")
        println()
        println("expected: \"${expected}\"")
        println("actual:   \"${actual}\"")
    }
    println()
}

fun main(args: Array<String>) {
    if ((args.size == 1) && (args[0] == "test")) {
        testAll()
    } else {
        solve()
        writer.flush()
    }
}

///////////////////////////////////////////////////////////

fun testAll() {
    debug = true

    test(1,
    """
    4 5
    3 2 4 1
    """,
    "4")
    test(2,
    """
    6 727202214173249351
    6 5 2 5 3 2
    """,
    "2")
}

fun solve() {
    val (_, K) = nextLongs()
    val towns = nextInts()

    val visited = mutableMapOf<Int, Long>()
    var t = 1
    var first = 0L
    var second = 0L
    for (i in 0 until K) {
        if (visited.containsKey(t)) {
            first = visited[t]!!
            second = i
            break;
        }
        visited.put(t, i)
        t = towns[t-1]
    }

    val len = second - first
    val remain = (K - first) % len
    for (i in 0 until remain) {
        t = towns[t-1]
    }

    put(t)
}