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: Wrong Answer)

import java.util.HashMap;
import java.util.Scanner;

// https://atcoder.jp/contests/abc167/tasks/abc167_d
public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long k = sc.nextLong();
		int[] array = new int[n+1];
		for (int i = 0; i < n; i++) {
			array[i] = sc.nextInt();
		}
		sc.close();

		int end = 0;

		array[n] = 1;
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		int tmp = 1;
		map.put(tmp, 0);
		for (int i = 1; i <= n+1; i++) {
			tmp = array[tmp - 1];
			if (map.containsKey(tmp)) {
				end = i;
				break;
			} else {
				map.put(tmp, i);
			}
		}

		long start = 0L;

		int tmp1 = 1;
		for(int i = 0;i<=n+1;i++) {
			if(i==0) {
				tmp1 = array[n];
			}else {
				tmp1 = array[tmp1-1];
			}
			if(tmp1==tmp) {
				start = i;
				break;
			}
		}
		long rep = end - start;

		int ans = 1;
		long aa = k - start;
		for(int i = 1;i<=start+aa%rep;i++) {
			ans = array[ans-1];
		}
		System.out.println(ans);
	}
}