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>
#define fi        first
#define se        second
#define pb        push_back
#define PI        acos(-1)
#define LC(a)     ((a<<1))
#define RC(a)     ((a<<1)+1)
#define MID(a,b)  ((a+b)>>1)
#define mem(a, b) memset(a, b, sizeof(a))
#define IOS()     std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
using namespace std;
typedef long long ll;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<ll,ll>   PLL;
const int INF = 0X3F3F3F3F;
const int MIN = -(1<<30);
const ll N = 2e5+7;
int a[N],b[N];
inline void solve()
{
	ll n,k;cin>>n>>k;
	queue<int> que; que.push(1);
	map<int,int> mp;mp[1]=0;
	for(int i=1;i<=n;i++) cin>>a[i];
	int x= a[1];
	for(int i=1;i<=n;i++)
	{
		if(!mp.count(x)) mp[x] = i,que.push(x),x=a[x];
		else 
		{
			while(que.front()!=x)
			{
				k--;
				que.pop();
			}
			k++;
			ll p = k%que.size();
			if(p==0) p=que.size();
			
			int cnt = 1;
			while(que.size())
			{
				if(cnt == p)
				{
					cout<<que.front()<<endl;
					break;
				}
				que.pop();
				cnt++;
			}
			break;
		}
		
	}
}
int main()
{
	IOS();
	solve();
	return 0;
}