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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.util.function.Function;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long k = sc.nextLong();
        int[] ai = new int[n];
        for (int i=0; i<n; i++) {
            ai[i] = sc.nextInt();
        }

        Function<Integer, Integer> teleport = i -> ai[i-1];
        List<Integer> alreadyVisit = new ArrayList<>();
        Integer now = 1;
        alreadyVisit.add(now);
        for (long i=0; i<k; i++) {
            now = teleport.apply(now);
            if (alreadyVisit.contains(now)) {
                int firstCount = alreadyVisit.indexOf(now);
                int loopCount = alreadyVisit.size() - firstCount;
                now = alreadyVisit.get((int)((k-firstCount) % loopCount) + firstCount);
                break;
            } else {
                alreadyVisit.add(now);
            }
        }
        System.out.println(now);
    }
}