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: Runtime Error)

#include <stdio.h>

int main(){
  long long n,k,d,c,e,f;
  scanf("%lld%lld",&n,&k);
  
  long long a[n+1],b[n+1];
  for(int i=1;i<=n;i++){
    scanf("%lld",&a[i]);
    b[i]=0;
  }
  
  c=a[1];
  b[1]=1;
  
  for(int i=1;i<=n;i++){
    c=a[c];
    b[c]+=1;
    if(b[c]==2){d=i;e=c;break;}
  }
  
   c=a[1];
  
  for(int i=1;i<=n;i++){
    c=a[c];
    if(c==e){f=i;break;}
  }
  
  c=a[e];
  k=(k-f+1)%(d-f);
  
  if(k==0){printf("%lld",e);return 0;}
  
  for(int i=1;i<=k;i++){
    c=a[c];
  }
  
  printf("%lld",c);
  return 0;
}