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.ArrayList;
import java.util.List;
import java.util.Scanner;
 
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Integer town = sc.nextInt();
		Long teleport = sc.nextLong();
 
		List<Integer> lists = new ArrayList<Integer>(town);
		for(int i = 0; i < town; i ++) {
			lists.add(sc.nextInt() - 1);
		}
 
		List<Integer> teleLists = new ArrayList<Integer>(town);
		Integer nowTown = 0;
		Integer nextTown = 0;
		teleLists.add(0);
		while(true) {
			nextTown = lists.get(nowTown);
			if(teleLists.contains(nextTown)) {
				break;
			}
			teleLists.add(nextTown);
			nowTown = nextTown;
		}
 
		Integer roopStart = teleLists.indexOf(nextTown);
		Long num1 = teleport - roopStart;
		
		Integer roopRemain = (int) (num1 % (teleLists.size() - roopStart));
		Integer result = teleLists.get(roopStart + roopRemain) + 1;
		
		System.out.println(result);
	}
}