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: Time Limit Exceeded)

import sys

n, k = map(int, input().split())
A = list(map(int, input().split()))

L = [1]
tmp = 1
ct = 0
check = 0
while True:
    x = A[tmp - 1]
    ct += 1
    if x in L or ct > k:
        check = x
        break
    else:
        L.append(x)
        tmp = x
if ct > k:
    print(L[k])
    sys.exit()
p = L.index(check)
l = len(L)
roop = l - p
if k < p:
    print(L[k])
else:
    k -= p
    k %= roop
    print(L[p + k])