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


	public class Main {
		

		public static void main(String[] args) {

			Scanner sc = new Scanner(System.in);
	        
			int n = sc.nextInt();
			long k = sc.nextLong();
			int[] a = new int[n];
			int now = 0;
			Map<Integer,Integer> m = new HashMap<Integer,Integer>();
			int cyc = 0;
			int start = 0;
			
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
			}
			
			m.put(0, 0);
			
			for(int i=1;i<n;i++) {
				now = a[now]-1;
				
				if(m.containsKey(now)) {
					start = m.get(now);
					cyc = i-m.get(now);;
					break;
				}else {
					m.put(now, i);
				}
			}

			
			long lstart = start;
			long lcyc = cyc;
			
			long cal = 0;
				cal =(k-lstart)%lcyc;
			
			long xx = lstart+cal;
			int now2 = 0;
			for(int i=0;i<xx;i++) {
				now2=a[now2]-1;
			}
			
			
			System.out.println(now2+1);
			
		}
		
		
	}