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()))
import numpy as np
link = set()
next = a[0]
link.add(1)
while next not in link:
    link.add(next)
    next = a[next-1]

link2 = set()
next2 = a[0]
link2.add(1)
while next not in link2:
    link2.add(next2)
    next2 = a[next2-1]

link2.remove(next)
ans = 0

rep = len(link)- len(link2)

if(k > len(link2)):
    p = (k-len(link2))%rep
    for i in range(p):
        next = a[next-1]
else:
    next = 0
    for i in range(k-1):
        next = a[next-1]

ans = next
print(ans)