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;

int main(void){
    int N;
    int64_t K;
    cin >> N >> K;
    vector<pair<int, int>> A(N);
    for (int i = 0; i < N; i++) {
        int x;
        cin >> x;
        A.at(i) = make_pair(--x, 0);
    }
    
    int count = 0;
    int ptr = A.at(0).first;
    for (;;) {
        ptr = A.at(ptr).first;
        A.at(ptr).second++;
        count ++;
        if (A.at(ptr).second >= 2) {
            count--;
            break;
        }
    }
    int count2;
    for (int i = 0; i < N; i++) {
        if (A.at(i).second == 1) {
            count2++;
        }
    }
    count -= count2;
    K %= count;
    for (int64_t i = 0; i < K - 1; i++) {
        ptr = A.at(ptr).first;
    }
    cout << ptr + 1 << endl;
    
    
}