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.*;

public class Main{
    void solve(){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        long k = scan.nextLong();
        int[] a = new int[n];
        for(int i = 0; i < n; i++) a[i] = scan.nextInt() - 1;
        int c = 1;
        int index = 0;
        List<Integer> loop = new ArrayList<>();
        TreeSet<Integer> seen = new TreeSet<>();
        loop.add(0);
        seen.add(0);
        while(!seen.contains(a[index])){
            loop.add(a[index]);
            seen.add(a[index]);
            index = a[index];
            c++;
        }
        int start = loop.indexOf(a[index]) + 1;
        c -= loop.size() - start;
        System.out.println(loop.get((int)(k % c)) + 1);
    }

    public static void main(String[] args){
        new Main().solve();
    }
}