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()))

limit = K
now = 1
log = []

while limit > 0 and now not in log:
    if 1 not in log:
        log.append(1)
    #print("通過1",now,limit,log)
    now = A[now - 1]
    log.append(now)
    limit -= 1

if limit > 0:
    #print("通過2",now,limit,log)
    limit = limit % len(log[log.index(now) - 1:])

    while limit > 0:
        #print("通過3",now)
        now = A[now - 1]
        limit -= 1

now = A[now - 1]

print(now)