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: Time Limit Exceeded)

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

namespace AtCoder.R167.D
{
    public static class Solver
    {
        public static void Main()
        {
            using (var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Solve(Console.In, sw);
            }
        }

        public static void Solve(TextReader tr, TextWriter tw)
        {
            WriteAnswer(tw, Parse(tr));
        }

        private static void WriteAnswer(TextWriter tw, int answer)
        {
            tw.WriteLine(answer);
        }

        private static int Parse(TextReader tr)
        {
            var w = tr.ReadLine().Split().Select(c => long.Parse(c)).ToArray();
            var k = w[1];
            var a = tr.ReadLine().Split().Select(c => int.Parse(c) - 1).ToArray();
            
            return Calc(k, a);
        }

        public static int Calc(long k, int[] a)
        {
            var visited = new List<int>();

            var current = 0;
            for (var i = 0L; i < k; ++i)
            {
                if (visited.Contains(current))
                {
                    var c = visited.IndexOf(current);
                    var r = visited.Count - c;
                    return visited[(int)(c + (k - c) % r)] + 1;
                }
                visited.Add(current);
                current = a[current];
            }
            return current + 1;
        }
    }
}