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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define ll long long

int main() {
  ll n,k=0;
  cin>>n>>k;
  vector<ll> vec(n);
  ll now=0;
  for(ll i=0;i<n;i++){
    cin>>vec.at(i);
  }
  vector<ll> nowvec(n);
  ll loop,loopStart,untilLoop=0;
  bool looped=false;
  
  for(ll i=0;i<k;i++){
    nowvec.at(i)=now;
    now=vec.at(now)-1;
    //nowvec.at(i)=now;	
    for(ll j=0;j+1<i;j++){
      if(nowvec.at(j)==now){
        loop=i-j+1;
        loopStart=now;
        untilLoop=j;
        looped=true;
        break;
      }
    }
    if(looped){
      break;
    }
  }
  
  
  
  if(looped){
    //cout<<loop;
    k-=untilLoop;
    //cout<<loopStart<<endl;loopStartはOK
    //cout<<untilLoop<<endl;
    k=k%loop;
    //cout<<k<<endl;
    now=loopStart;
    //cout<<now<<endl;
    for(ll i=0;i<k;i++){
      now=vec.at(now)-1;
      cout<<now<<endl;
    }
  }
  cout<<now+1;
}