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 Python (3.8.2) (judge verdict: Accepted)

import numpy as np

def main():
    n, k = map(int, input().split())
    a = list(map(lambda x: int(x)-1, input().split()))
    foot = [0]
    is_loop = False
    ed = np.zeros([n], dtype=int)
    ed[0] = 1

    for i in range(1,k):
        go = a[foot[-1]]
        foot.append(go)
        if ed[go] == 1:
            st_i = foot.index(foot[-1])
            lo_size = len(foot)-1 - st_i

            k -= st_i
            k %= lo_size
            
            print(foot[st_i+k]+1)
            is_loop = True
            break
        ed[go] = 1
    
    if not is_loop:
        print(a[foot[-1]]+1)


if __name__ == '__main__':
    main()