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.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming {
  public void Solve() {
    var(N, K) = Cin<int, long>();
    var A = Cinarr<int>().Select(x => x - 1).ToArray();
    var hs = new Dictionary<int, int>();
    var turn = 0;
    int cur = 0;
    int cnt = 0;
    var hsnext = 0;
    hs[0] = 0;
    while (true) {
      var next = A[cur];
      ++cnt;
      if (hs.ContainsKey(next)) {
        turn = cnt - hs[next];
        hsnext = hs[next];
        break;
      }
      hs[next] = cnt;
      cur = next;
    }
    var posi = 0;
    for (int i = 0; i < cnt; ++i) {
      --K;
      posi = A[posi];
    }
    K = (K + turn) % turn;
    for (int i = 0; i < K; ++i) {
      posi = A[posi];
    }
    Put(posi + 1);

  }

}

public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv(Deno)) % MOD;
  }
  public static long Comb2(long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv(long x, int MOD = 1000000007) {
    return Power(x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T>(ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(string N) {

    int ret = 0;
    for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
    return ret;
  }
  public static string ConvertBase(long N, int K) {
    StringBuilder ret = new StringBuilder();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append(r);
    }
    return new string(ret.ToString().ToCharArray().Reverse().ToArray());
  }
}
class Program {
  static void Main(string[] args) {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io {

  public static void Put(string a) => Console.WriteLine(a);
  public static void Put(params object[] i) => Put(string.Join(" ", i));
  public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
  public static void PutV<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
  public static void YN(bool i) {
    if (i) Put("Yes");
    else Put("No");
  }
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
  public static T ConvertType<T, U>(U a) => (T) Convert.ChangeType(a, typeof(T));
  public static T Cast<T>(string s) {
    if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
    else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
    else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
    else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
    else return ConvertType<T, string>(s);
  }
  public static T[] Castarr<T>(string[] s) {
    var ret = new T[s.Length];
    int i = 0;
    foreach (var t in s) {
      if (IsTypeEqual<T, int>()) ret[i++] = ConvertType<T, int>(int.Parse(t));
      else if (IsTypeEqual<T, long>()) ret[i++] = ConvertType<T, long>(long.Parse(t));
      else if (IsTypeEqual<T, double>()) ret[i++] = ConvertType<T, double>(double.Parse(t));
      else if (IsTypeEqual<T, char>()) ret[i++] = ConvertType<T, char>(char.Parse(t));
      else ret[i++] = ConvertType<T, string>(t);
    }
    return ret;
  }
  public static T Cin<T>() { var t = Strs; return (Cast<T>(t[0])); }
  public static(T, U) Cin<T, U>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1])); }
  public static(T, U, V) Cin<T, U, V>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2])); }
  public static(T, U, V, W) Cin<T, U, V, W>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3])); }
  public static(T, U, V, W, X) Cin<T, U, V, W, X>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4])); }
  public static(T, U, V, W, X, Y) Cin<T, U, V, W, X, Y>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5])); }
  public static(T, U, V, W, X, Y, Z) Cin<T, U, V, W, X, Y, Z>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5]), Cast<Z>(t[6])); }
  public static T[] Cinarr<T>() { var t = Strs; return Castarr<T>(t); }
  public static T[] CinV<T>(int n) {
    var ret = new T[n];
    for (int i = 0; i < n; ++i) {
      ret[i] = Cin<T>();
    }
    return ret;
  }
}