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 PyPy3 (7.3.0) (judge verdict: Accepted)

N, K = map(int, input().split())
As = list(map(int, input().split()))

appeared = [False] * N
appeared[0] = True
path = [1]
for _ in range(N+10):
    next_A = As[path[-1] - 1]
    if appeared[next_A-1]:
        break
    else:
        path.append(next_A)
        appeared[next_A-1] = True

before_loop = path.index(next_A)
loop_len = len(path) - before_loop

if K <= before_loop:
    print(path[K])
else:
    print(path[(K - before_loop) % loop_len + before_loop])