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

ans = A[0]

d = {0:1, ans -1:1}
#移動する可能性がある街の個数uを出す
for i in range(2 * N):
  #print(ans)
  ans = A[ans - 1]
  if ans -1 not in d:
    d[ans -1] = 1
  else:
    d[ans - 1] += 1
  
#print("d", d, len(d))
u = len(d)

if d[0] == 1:
  a = (K - 1) % u
else:
  a = K % u
if a == 0:
  a = u
  
#print("a", a)
ans = A[A[0] - 1]
for i in range(a + 1):
  #print(i, ans)
  ans = A[ans - 1]
print(ans)