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>
#define rep(i,n) for (int i = 0;i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

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

  vector<int> s;
  vector<int> ord(n+1, -1);
  int c = 1, l = 0;
  {
    int v = 1;
    while (ord[v] == -1) {
      ord[v] = s.size();
      s.push_back(v);
      v = a[v-1];
    }
    c = s.size() - ord[v];
    l = ord[v];
  }

  if (k < l) cout << s[k] << endl;
  else {
    k -= l;
    k %= c;
    cout << s[l+k] << endl;
  }
  return 0;
}