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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nk = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var towns = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var tree = towns.Select(x => new Node()).ToArray();
            var first = towns[0];
            for (var i = 0; i < tree.Length; i++)
            {
                tree[i].Index = i;
                tree[i].Next = tree[towns[i] - 1];
            }
            var counter = new int[tree.Length];
            var index = 0;
            while (true)
            {
                counter[index]++;
                if (counter[index] == 3) break;
                index = tree[index].Next.Index;
            }
            var loopCount = 0L;
            var stepCount = 0L;
            for (var i = 0; i < counter.Length; i++)
            {
                if (counter[i] >= 2) loopCount++;
                if (counter[i] > 0) stepCount++;
            }
            var tmp = nk[1] - stepCount;
            var end = tmp % loopCount;
            var answer = 0L;
            for (var i = 0; i <= end; i++)
            {
                answer = tree[index].Index + 1;
                index = tree[index].Next.Index;
            }
            Console.WriteLine(answer);
        }

        public class Node
        {
            public int Index { get; set; }
            public Node Next { get; set; }
        }
    }
}