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>
using namespace std;

//解説AC

int main(){
    int n;
    long long k;
    cin >> n >> k;
    vector<int> a(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
        a[i]--;
    }
    
    deque<int> b;
    vector<bool> seen(n,false);
    int tmp = 0;
    while(true){
        if(seen[tmp]){
            while(b[0] != tmp){
                k--;
                b.pop_front();

                if(k == 0){
                    cout << a[0] + 1 << endl;
                    return 0;
                }
            }
            break;
        }
        b.push_back(tmp);
        seen[tmp] = true;
        tmp = a[tmp];
    }
    cout << b[k % b.size()] + 1 << endl;

    return 0;
}