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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    
    public static void main(String[] args) throws Exception{

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        long k = sc.nextLong();

        int[] a = new int[n];
        for(int i=0; i<n; i++){
            a[i] = sc.nextInt();
        }

        List<Integer> list = new ArrayList<>();
        list.add(a[0]);
        int num = 0;
        for(int j=0; j<n; j++){
            int i = list.get(list.size() - 1);
            if(a[i - 1] == 1){
                break;
            }
            else if(list.contains(a[i - 1])){
                num = list.indexOf(a[i - 1]);
                break;
            }
            list.add(a[i - 1]);
        }

        long r = (k - num) % ((long)list.size() + num);
        System.out.println(list.get((int)r));
    }
}