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() = abc167d()

@OptIn(ExperimentalStdlibApi::class)
fun abc167d() {
    var (n, k) = readLine()!!.split(' ').map { it.toLong() }
    val aList = readLine()!!.split(' ').map { it.toInt() - 1 }.toIntArray()

    val visited = mutableSetOf(0)
    val indices = IntArray(n.toInt())
    indices[0] = 0

    var outerLoop = 0
    var curr = 0

    while (--k >= 0) {
        curr = aList[curr]
        if (!visited.add(curr)) break

        outerLoop++
        indices[curr] = outerLoop
    }

    if (k == -1L) return println(curr + 1)

    val visitedInLoop = mutableSetOf<Int>()
    var loopLength = 0
    val path = IntArray(n.toInt()) { -1 }

    repeat(n.toInt()) {
        if (visitedInLoop.add(curr)) {
            path[curr] = loopLength
            loopLength++
            curr = aList[curr]
        }
    }

    val answer = path.indexOf((k % loopLength).toInt()) + 1

    println(answer)
}