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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
 
 class Program
    {
        static void Main(string[] args)
        {
            string[] inputA = Console.ReadLine().Split(' ');
            string[] inputB = Console.ReadLine().Split(' ');
            var list = new List<int>();
            int len = int.Parse(inputA[0]);
            long k = long.Parse(inputA[1]);
            int[] arr = inputB.Select(s => int.Parse(s)).ToArray();
            int nowInd = 0;
            int nowValue = arr[nowInd];
            int findInd = 0;
            long a = 0;
            bool bln = false;
            list.Add(nowInd+1);
            for (long i = 2; i <= k; i++)
            {
                nowInd = nowValue - 1;
                nowValue = arr[nowInd];
                if(list.Contains(nowValue))bln = true;
                list.Add(nowInd + 1);
                if (bln)
                {
                  	findInd = list.FindIndex(n => n == nowValue);
                    a = (k - findInd) % (i - findInd) + findInd;
                    Console.WriteLine(list[(int)a]);
                    return;
                }
            }
            Console.WriteLine(nowValue);
        }
}