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) = readLine()!!.split(' ').let { it[0].toInt() to it[1].toLong() }
    val a = readLine()!!.split(' ').map { it.toInt() - 1 }
    val b = IntArray(n) { -1 }
    b[0] = 0

    var cur = 0
    var flag = false
    var x = k

    while (x > 0) {
        x--
        val next = a[cur]

        if (flag) {
            cur = next
            continue
        }

        if (b[next] == -1) {
            b[next] = b[cur] + 1
            cur = next
            continue
        }

        flag = true
        x %= (b[cur] + 1 - b[next])
        cur = next
    }

    println(cur + 1)
}