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 t = Array(60) { IntArray(n + 1) }
    t[0] = IntArray(1) + readLine()!!.split(' ').map { it.toInt() }.toIntArray()

    for (i in 0 until 59) {
        for (j in 1..n) {
            t[i + 1][j] = t[i][t[i][j]]
        }
    }

    val ans = run {
        var k = K
        var v = 1
        for (i in (0 until 60).reversed()) {
            val l = 1L shl i
            if (l <= k) {
                v = t[i][v]
                k -= l
            }
        }
        v
    }

    println(ans)
}