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)

import java.io.PrintWriter
import java.util.ArrayDeque

fun main() {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

fun solve(out: PrintWriter) {
    val (n, k) = readLongList()
    val aList = readIntegerList().map { it - 1 }
    val count = IntArray(n.toInt()) { -1 }
    var cur = 0
    var i = 0
    while (true) {
        if (count[cur] != -1) {
            break
        }

        count[cur] = i
        i++
        cur = aList[cur]
    }

    if (k - count[cur] < 0) {
        cur = 0
        repeat(k.toInt()) {
            cur = aList[cur]
        }
        println(cur + 1)
    } else {
        val tmp = i - count[cur]
        val tmp2 = (k - count[cur]) % tmp

        repeat(tmp2.toInt()) {
            cur = aList[cur]
        }
        println(cur + 1)
    }
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)