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.*;
public class Main {

  public static void main(String[] args) { 
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      long k = sc.nextLong();
      int[] arr = new int[n+1];
      for(int i = 1; i <= n; i++)
        arr[i] = sc.nextInt();

      int fast = 1;
      int slow = 1;
      long moves = 0;
      while(true) {
        fast = arr[arr[fast]];
        slow = arr[slow];
        moves++;
        if(fast == slow) break;
      }

      
      fast = 1;
      
      while(k > 0) {
        fast = arr[fast];
        slow = arr[slow];
        k--;
        if(fast == slow) break;
      }

      int entryEle = fast;
      
      if(k > 0) {
        int res = fast;
        long step = k % moves;
        for(long i = 0; i < step; i++)
          res = arr[res];
        System.out.println(res);
      } else {
        System.out.println(slow);
      }
      
      
  }
}