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: Accepted)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
    	int n = sc.nextInt();
    	long k = sc.nextLong();
    	Map<Integer,Integer> teleport = new HashMap<>();
    	Map<Integer,Long> history = new HashMap<>();
    	for(int i = 1 ; i <= n; i++){
    		teleport.put(i, sc.nextInt());
    	}
    	long i;
    	int now = 1;
    	boolean flag = false;
    	for(i = 0; i <= k; i++){
    		if(history.containsKey(now)){
    			flag = true;
    			break;
    		}
    		history.put(now, i);
    		now = teleport.get(now);
    	}
    	if(flag){
    		long pastTime = history.get(now);
    		k = pastTime + (k - pastTime) % (i - pastTime);
    	}
    	for(int p : history.keySet()){
    		if(history.get(p) == k){
    			System.out.println(p);
    			return;
    		}
    	}
    }
}