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: Runtime Error)

#include <algorithm>
#include <iostream>
#include <set>
#include <vector>

using namespace std;
using ll = long long;

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

int main() {
  int n;
  ll k;
  cin >> n >> k;
  int a[n];
  rep(i, n) {
    cin >> a[i];
    --a[i];
  }

  vector<int> d;
  d.push_back(0);
  set<int> v;
  int loop = 0;
  for (int i = 0; i < n - 1; ++i) {
    int nx = a[d[i]];
    if (v.find(nx) != v.end()) {
      loop = d.size() - distance(d.begin(), find(d.begin(), d.end(), nx));
      break;
    }
    d.push_back(nx);
    v.insert(nx);
  }

  int noLoop = d.size() - loop;
  int ans = d[noLoop + (k - noLoop) % loop];
  cout << ++ans << '\n';

  return 0;
}