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: Wrong Answer)

N, K = map(int, input().split())
A = list(map(int, input().split()))
#N=6
#K=1
#A=[6,5,2,5,3,2]
iti = 1
ex_A = []
basyo=0

for k in range(K):
    ex_A.append(iti)
    iti = A[iti-1]
    if iti in ex_A:
        basyo = ex_A.index(iti)
        maru = len(ex_A[:basyo])
        nokori = (K - maru) % len(ex_A[basyo:])
        break

if basyo:
    iti = ex_A[basyo+nokori]
#print(ex_A)
print(iti)