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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <math.h>

#define ll long long int
#define mod 1000000007

using namespace std;


int main()
{
    ios_base::sync_with_stdio(false); 
    cin.tie(NULL);
  
  ll n, k;
  cin >> n >> k;
  vector<pair<ll,bool>> vec;
  for(ll i = 0; i < n;i++){
      ll x;
      cin >> x;
      vec.push_back(make_pair(x,false));
  }
  if(k <= n){
       int i = 0;
  ll x = 0;
    for(;x < k;x++){
          i = vec[i].first - 1;
       
    }
    cout << i+1;
  }
  else{
  int i = 0;
  ll x = 0;
    for(;x < k;x++){
      if(vec[i].second == false){
          vec[i].second = true;
          i = vec[i].first - 1;
         
          
      }
      else
      break;
  }
  for(ll b = 0;b<vec.size();b++){
      vec[b].second = false;
  }
 
  ll p =0;
  for(;p<k;p++){
       if(vec[i].second == false){
          vec[i].second = true;
          i = vec[i].first - 1;
         
          
      }
      else
      break;
  }
  k = k-x;
  k = k%p;
  
  for(ll q = 1;q<=k;q++){
      i = vec[i].first - 1;
  }
  cout << i+1;
  }
  
}