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()
}

fun abc167d() {
    val (n, k) = readLine()!!.split(" ").map { it.toLong() }
    val town = readLine()!!.split(" ").map { it.toInt() - 1 }
    var i = 0
    val visited = mutableSetOf<Int>(0)
    var isLooped = false
    var checkLooped = false
    var count = 0
    var loopReturnedNum = 0
    while (!checkLooped && count < n) {
        i = town[i]
        count++
        if (visited.contains(i)) {
            checkLooped = true
            loopReturnedNum = i
        } else {
            visited.add(i)
        }
    }
    val loopedCount = count
    var cycleCount = 0
    if (checkLooped) {
        count = 0
        while (!isLooped) {
            i = town[i]
            count ++
            if (i == loopReturnedNum) {
                cycleCount = count
                isLooped = true
            }
        }
    }
    val startCount = loopedCount - cycleCount
    val t = ((k - startCount) % cycleCount.toLong())
    i = 0
    if (startCount > k) {
        repeat(k.toInt()) {
            i = town[i]
        }
        println(i + 1)
    } else {
        repeat(t.toInt() + startCount) {
            i = town[i]
        }
        println(i + 1)
    }
}