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.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int townNum = scan.nextInt();
        long loveInt = scan.nextLong();
        Town[] towns = new Town[townNum + 1];
        for (int i = 1; i < townNum + 1; i++) {
            towns[i] = new Town(i);
        }

        for (int i = 1; i < townNum + 1; i++) {
            towns[i].setNextTown(towns[scan.nextInt()]);
        }

        towns[1].reach(1);
        Town endTown = towns[1].endlessGoNext();

        int startLoop=endTown.goNext().getFirstReach();
        int loop=endTown.getFirstReach()-startLoop+1;

        long minStep=loveInt;
        if (loveInt>startLoop){
            minStep=(loveInt-startLoop) % loop+startLoop;
        }

        Town end=towns[1];
        for (int i = 0; i <minStep ; i++) {
            end=end.goNext();
        }

        System.out.println(end.getId());
    }
}

class Town {
    private final int id;
    private int firstReach = 0;
    private Town nextTown;

    public Town(int id) {
        this.id = id;
    }

    public int getId() {
        return id;
    }

    public void setNextTown(Town nextTown) {
        this.nextTown = nextTown;
    }

    public boolean reach(int firstReach) {
        if (this.firstReach == 0) {
            this.firstReach = firstReach;
            return true;
        } else {
            return false;
        }
    }

    public int getFirstReach() {
        return firstReach;
    }

    Town goNext() {
        return nextTown;
    }

    Town endlessGoNext() {
        if (nextTown.reach(firstReach + 1)) {
            return nextTown.endlessGoNext();
        } else {
            return this;
        }
    }
}