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: Accepted)

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

class program
{
    static void Main()
    {
        var nk = Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();
        long n = nk[0], k = nk[1];
        var a = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var tel = new List<int>();
        var istel = new int[n];
        tel.Add(0);
        int rst = 0, pre = 0;
        for (int i = 1; i <= k; i++)
        {
            pre = a[pre] - 1;
            if (istel[pre] == 0)
            {
                tel.Add(pre);
                istel[pre] = i;
            }
            else
            {
                int roop = i - istel[pre];
                long ansid = ((k - istel[pre]) % roop);
                Console.WriteLine(tel[(int)ansid + istel[pre]] + 1);
                return;
            }
        }
        Console.WriteLine(tel.Last() + 1);
    }
}