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: Time Limit Exceeded)

import java.util.*;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    int n = sc.nextInt();
    long k = sc.nextLong();
    int[] a = new int[n];
    ArrayList<Integer> order = new ArrayList<>(); 
    order.add(1);
    int tmp = 0;
    boolean bool = true;
    int ans = 0;
    int j = 0;

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

    while(bool){
      if(order.contains(a[j]) == false){
       order.add(a[j]);
       j = a[j] - 1;
       } else {
        tmp = a[j];
        bool = false;
        break;
      }
    }

    int index = order.indexOf(tmp);
    int roop = order.size() - index;


    if(k <= index){
      ans = order.get((int)k);
    } else {
      ans = order.get(index + (int)((k - index) % roop));
    }

    System.out.println(ans);

  }
}