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.Scanner;

public class Main {
    public static void main(String[] args) {
        //コード
    	Scanner sc = new Scanner(System.in);
//    	File file = new File("src/in.txt");
//    	Scanner sc = new Scanner(file);
    	int N = sc.nextInt();
    	long K = sc.nextLong();
    	int[] A = new int[N+1];
    	for(int i=1;i<=N;i++) {
    		A[i] = sc.nextInt();
    	}

    	int[] history = new int[N+1];
    	history[0] = 1;
    	int now = 1;
    	int count = 0;
    	while (count<N) {
    		count = count+1;
    		now = A[now];
    		history[count] = now;
    	}
    	int loopstart = 0;
    	int loopend = 0;
//    	System.out.println("a");
    	for(int i = 0;i<N;i++){
    		for(int j = i+1;j<N;j++) {
    			if(history[i]==history[j]) {
    				loopstart = i;
    				loopend = j;
    				break;
    			}
    		}
    	}
    	int loop = loopend - loopstart;
//    	System.out.println("start->"+loopstart+"end->"+loopend);
    	long looptime = K -loopstart;
    	int q = (int) (looptime % loop);
    	System.out.println(history[loopstart+q]);

    }
}