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: Runtime Error)

N, K = map(int,input().split())
A = list(map(int,input().split()))
B = [0]
S = set([]);S.add(0)
now = 0
Flag = False
loop_start = -1
if K <= 2*pow(10,5)+10:
  for i in range(K):
    nxt = A[now]-1
    B.append(nxt)
    now = nxt
  #print(B)
  print(B[K]+1)
  exit()
for i in range(K*2):
  nxt = A[now]-1
  #print(now,nxt)
  if nxt in S:
    if Flag:
      if nxt == loop_start:
        #print(nxt,i)
        loop_cycle = i-loop_num
        break
    else:
      loop_start = nxt
      loop_num = i
      Flag = True
  else:
    B.append(nxt);S.add(nxt)
  now = nxt
#print(B,loop_start,loop_cycle,loop_num)
loc = (K-loop_start)%loop_cycle+loop_start
#print(loc)
print(B[loc]+1)