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.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		long k = s.nextLong();
		int[] a = new int[n + 1];
		for(int i = 0; i < n; i++) {
			a[i + 1] = s.nextInt();
		}
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		int start = 1;
		while(!map.containsKey(start) && k > 0) {
			map.put(start, map.size());
			start = a[start];
			k--;
		}
		if(k == 0) {
			System.out.println(start);
			return;
		}
		k %= (map.size() - map.get(start));
		map.clear();
//		System.out.println(map);
		while(!map.containsKey(start) && k > 0) {
			map.put(start, map.size());
			start = a[start];
			k--;
		}
		System.out.println(start);
	}

}