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() {
    val (n, k) = run {
        val (n, k) = readLine()!!.split(' ').map { it.toLong() }
        n.toInt() to k
    }
    val a = readLine()!!.split(' ').map { it.toInt() }

    val (s, l, c) = run {
        val r = mutableListOf<Int>()
        val visited = IntArray(n + 1) { -1 }

        var v = 1
        while (visited[v] == -1) {
            visited[v] = r.size
            r.add(v)
            v = a[v - 1]
        }

        val l = visited[v]
        val c = r.size - visited[v]
        Triple(r, l, c)
    }

    val i = if (k < l) {
        k.toInt()
    } else {
        ((k - l) % c).toInt() + l
    }

    println(s[i])
}