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 <bits/stdc++.h>
typedef long long int ll;
const ll N=2*1e5+10;
using namespace std;
ll a[N];


int main() {
	// your code goes here
	// ios_base::sync_with_stdio(false);
	// cin.tie(NULL);
	// cout.tie(NULL);
	ll n,k;
    cin>>n>>k;
   
    for(int i=1;i<=n;i++)
    cin>>a[i];
    vector<ll>c;
    vector<int>vis(n+1,0);
    int next=1;
    while(!vis[a[next]])
    {
    	vis[a[next]]=1;
    	c.push_back(a[next]);
    	next=a[next];
    }
    ll z=c.size();
    // for(auto i:c)
    // cout<<i<<"\n";
    if(k<=z)
    {
    	cout<<c[k-1];
    	return 0;
    }
   
    ll idx=0;
    for(int i=0;i<z;i++)
    {
    	if(c[i]==a[c[z-1]])
    	{
    		idx=i;
    		break;
    	}
    }
    ll size=k-idx;
  
    	ll r=size%(z-idx);
    	//cout<<r<<"\n";
    	
    	if(r==0)
    	cout<<c[z-1];
    	else
    	cout<<c[idx+r-1];
    
   
	
	
	return 0;
}