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 <algorithm>
#include <map>
#include <iostream>
#include <string>
#include <set>
#include <queue>
#include <cmath>
#include <iterator>
#include <array>
#include <iomanip>
typedef long long int ll;
using namespace std;
#define maxN 200005
#define mod 1000000007
#define pi 3.14159265358979323846264338327950

ll all[maxN] = {};
bool vis[maxN] = {};

void solve()
{
    ll n, k;
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
    {
        cin >> all[i];
    }
    vis[1] = true;
    int now = 1;
    while (1)
    {
        now = all[now];
        if (vis[now])
        {
            break;
        }
        vis[now] = true;
    }
    //cout<<"start: "<<now<<endl;
    int start = now;
    for (int i = 0; i <= n; i++)
    {
        vis[i] = 0;
    }
    vector<int> path;
    while (1)
    {
        path.push_back(start);
        vis[start] = true;
        start = all[start];
        if (vis[start])
        {
            break;
        }
    }
    //cout <<path.size() << endl;
    for (int i = 0; i <= n; i++)
    {
        vis[i] = 0;
    }
    int temp = 1;
    while (1)
    {
    	if(k==1){
    		cout<<temp<<endl;
    		return;
		}
    	if (temp == now)
        {
            break;
        }
        temp = all[temp];
        k--;
    }
    cout << path[k % path.size()] << endl;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    solve();
}