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: Runtime Error)

fun main() {
    val l = readLine()!!.split(" ")
    val n = l[0].toInt()
    val k = l[1].toLong()
    val array = readLine()!!.split(" ").map { it.toInt() - 1}
    val flags = Array(n){-1L}
    var current = 0
    var mod = 0L
    var remain = 0L
    for(i in 0..k-1){
        if(flags[current]!=-1L){
            mod = i-flags[current]
            remain = k-i
            break
        }
        flags[current] = i
        current = array[current]
    }
    val x = remain%mod
    if(x==0L) {
        println(current+1)
    }else{
        for(i in 0..x-1) {
            current = array[current]
        }
        println(current+1)
    }
}