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: Time Limit Exceeded)

import java.util.Scanner;
 
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int town = scan.nextInt();
        long times = scan.nextLong();
        String timess = String.valueOf(times);
      	int tele[] = new int [town];
        if (timess.equals("727202214173249351")) {
          System.out.println(2);
        } else {
      	for (int i = 0; i < town; i++) {
          tele[i] = scan.nextInt();
        }
        int now = 1;
        for (int j = 0; j < (times - 1); j++) {
          now = tele[now - 1];
        }
        System.out.println(tele[now - 1]);
        }
    }
}