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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int N;
long long K;
vector<int> A, T;

int main()
{
  cin >> N >> K;
  A.resize(N + 1);
  for (int i = 1; i <= N; i++)
  {
    cin >> A.at(i);
  }
  T.resize(N + 1, -1);
  int timer = 0;
  int next = 1;
  int loop_size, q;
  while (1)
  {
    if (T.at(next) != -1)
    {
      loop_size = timer - T.at(next);
      q = T.at(next);
      break;
    }
    T.at(next) = timer;
    next = A.at(next);
    timer++;
  }
  int loop_times = 0;
  if (K < q)
  {
    loop_times = K;
  }
  else
  {
    loop_times = ((K - q) % loop_size) + q;
  }
  int ans = 1;
  for (int i = 0; i < loop_times; i++)
  {
    ans = A.at(ans);
  }
  cout << ans << endl;
}