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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main() {
  long N,K;cin>>N>>K;
  vector<int> A(N);
  for(int i=0;i<N;i++) cin>>A.at(i);//　テレポーター指示
  vector<int> B(N+1,0);//これまで到着した町
  B.at(0)=1;
  long count=0;
  int temp=1;
  //long j=0;
  long J;
  //long J,X;
 /* while(count<N){
    count++;
    temp=A.at(temp-1);
    B.at(count)=temp;
    while(j<count){//これまで到着した街と、今count回目に到着した街が同じならループ
      if(B.at(j)==temp){
        J=j;
        X=count;
        count=N+1;
        break;
      }
      j++;
    }
    j=0;
  }
  // J<XかつB.at(J)==B.at(X)である、最初のペア
  long roop=X-J;
  long ans=(K-J)%roop+J;
  cout<<B.at(ans)<<endl; */
  bool can=true;
  int repeat;
  while(can){
    count++;
    temp=A.at(temp-1);
    B.at(count)=temp;
    for(int i=0;i<count;i++){
      if(B.at(i)==temp){
        can=false;
        J=i;
        break;
      }
    }
  }
  repeat=count-J;
  if(K>count){
    K -= count;
    long ans=(K%repeat)+J;
    cout<<B.at(ans)<<endl;
  }
  else cout<<B.at(K)<<endl;
}