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: Accepted)

import java.math.*;
import java.util.*;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		long n=sc.nextLong(),k=sc.nextLong();
		int arr[]=new int[(int) n+1];
//		int ans[]=new int[(int) n+1];
		for(int i=1;i<=n;i++){
			arr[i]=sc.nextInt();
		}
		HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
		int index=1;
		int count=1;
		while(!map.containsKey(arr[index])){
			map.put(arr[index], count);
//			ans[count]=index;
			count++;
			index=arr[index];
		}
		int cell=count-map.get(arr[index]);
		int form=map.get(arr[index]);
		if(k>=count){
			k-=count;
			k%=cell;
			k+=count;
			k-=cell;
		}
		for(int ts:map.keySet()){
//			System.out.println(ts+" "+map.get(ts));
			if(map.get(ts)==k){
				
				System.out.println(ts);
			}
		}
	}
}