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: Wrong Answer)

import java.util.*;
class Main{
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long k = scanner.nextLong();
        int[] a = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = scanner.nextInt()-1;
        }
        List<Integer> list = new ArrayList<>();
        int loophead = 0;
        boolean flag = false;
        list.add(0);
        int cur = a[0];
        for(int i = 1; i < n+1; i++){
            if(list.contains(cur)){
                loophead = cur;
                flag = true;
                break;
            }else{
                list.add(cur);
                cur = a[cur];
            }
        }
        if(!flag){System.out.println(cur);return;}
        int loopheadindex = list.indexOf(loophead);
        int looplength = list.size()-loopheadindex;
        /*
        System.out.println("list size " + list.size());
        System.out.println("head loop index " + loopheadindex);
        System.out.println("head loop length " + looplength);
        */
        long ansindex = (k - Long.valueOf(loopheadindex))%Long.valueOf(looplength);
        System.out.println(list.get((int)ansindex + loopheadindex) + 1);
    }
}