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: Time Limit Exceeded)

//20200510 D
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[] A=new int[N];
		for(int i=0;i<N;i++){
			A[i]=sc.nextInt()-1;
		}
		List<Integer> Q=new ArrayList<>();
		Q.add(0);
		int lsn;
		int len;
		while(true){
			int a=A[Q.get(Q.size()-1)];
			if(Q.contains(a)){
				lsn=Q.indexOf(a);
				len=Q.size()-1;
				break;
			}
			Q.add(a);
		}
      	/*for(Integer i:Q){
          System.out.println(i);
        }
      	System.out.println(lsn);
      	System.out.println(len);
      	System.out.println("");*/
		if(K<lsn){
			System.out.println(Q.get((int)K)+1);
		}else{
			int n=(int)((K-lsn)%(len-lsn+1))+lsn;
			System.out.println(Q.get(n)+1);
		}
	}
}