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 ll long long int
#define endl "\n"
#define mod 1000000007
#define ff first
#define ss second
#define pb push_back
using namespace std;

void solve(int test){
	ll n,k;
	cin>>n>>k;
	ll a[n];
	for (int i = 0; i < n; ++i)
	{
		cin>>a[i];
		a[i]--;
	}
	ll vis[n];
	memset(vis, -1, sizeof(vis));
	ll idx = a[0], cnt = 1;
	ll pos[n]={0};
	pos[0] = 0;
	vis[0] = 0;
	while(1){
		if (vis[idx] != -1)
		{
			break;
		}
		vis[idx] = cnt;
		pos[cnt] = idx;
		idx = a[idx];
		cnt++;
	}
	// for (int i = 0; i < n; ++i)
	// {
	// 	cout<<vis[i]<<" ";
	// }
	// cout<<endl;
	// for (int i = 0; i < n; ++i)
	// {
	// 	cout<<pos[i]<<" ";
	// }
	// cout<<endl;
	// cout<<cnt<<endl;
	if (k >= cnt - 1)
	{
		k -= (cnt - 1);
		k %= (cnt - vis[idx]);
		cout<<pos[vis[idx] - 1 + k] + 1;
	}
	else{
		cout<<pos[k] + 1	;
	}
}

int main(){
	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
	ll t=1,k;
	//cin>>t;
	k = t;
	while(t--){
		solve(k - t);
	}
	cerr<<"Timpe elapsed :" << clock() * 1000.0 / CLOCKS_PER_SEC << " mps\n" ;
	return 0;
}