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 <algorithm>
#include <iostream>
#include <map>
#include <string>
#include <vector>
#include <climits>
using namespace std;
using ll = long long;
int memo[(unsigned int)2e5];
int main() {
  int n; ll k;
  cin >> n >> k;
  vector<int> a(n);
  for (int i = 0; i < n; i++)
    cin >> a[i];
  //memo : その町がいくつ目の町か
  int next = 1;
  int it = 1;
  do {
    memo[next - 1] = it++;
    next = a[next - 1];
  } while (memo[next - 1] == 0 && it < k + 1);
  if (it == k + 1) {
    cout << next << endl;
    return 0;
  }
  int t = it - memo[next - 1];
  k -= memo[next - 1] - 1; //ループに入る前に通った町の数
  k %= t;
  while (k-- > 0) {
    next = a[next - 1];
  }
  cout << next << endl;
  return 0;
}