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.*;

public class Main {

    static int gcd (int a, int b) {return b>0?gcd(b,a%b):a;}
    static int mod = 1000000007;

    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];
        long[] teleported = new long[N];

        for(int i=0;i<N;i++){
            A[i] = sc.nextInt();
            teleported[i] = -1;
        }

        int currentPoint = 1;
        teleported[0] = 0;
        long warpCount = 0;
        long loop;
        long restOfLoop=0l;
        for(int i=0;i<N-1;i++){
            warpCount++;
            currentPoint = A[currentPoint-1];
            if(teleported[currentPoint-1] == -1){
                teleported[currentPoint-1] = warpCount;
            } else {
                loop = warpCount - teleported[currentPoint-1];
                restOfLoop = (K - teleported[currentPoint-1]) % loop;
                break;
            }
        }

        for(int i=0;i<restOfLoop;i++){
            currentPoint = A[currentPoint-1];
        }
        System.out.println(currentPoint);

    }

}