Buggy python submission (verdict: Time Limit Exceeded):
#Doubling O(log k)
def main():
  ## IMPORT MODULE
  #import sys

  #sys.setrecursionlimit(100000)
  #input=lambda :sys.stdin.readline().rstrip()

  #f_inf=float("inf")
  #MOD=10**9+7
  
  if 'get_ipython' in globals(): 
    ## SAMPLE INPUT
    n, k = 4, 5
    A = [3, 2, 4, 1]

  else:
    ##INPUT 
    #n = input()
    n, k = map(int, input().split())
    A = list(map(int, input().split()))

  ## SUBMITION CODES HERE
  D = 60 # 10^18 is 60 digits, so we'll see to the 59th power of 2.
  MAX_N = 200005 #Namber of nodes
  to = [[0 for _ in range(MAX_N)] for _ in range(D)]

  # to[i][j]:nodes to 2^i away from j  
  for i in range(n):
    to[0][i] = A[i]
    to[0][i] -= 1

  # Doubling matrix
  for i in range(D-1):
    for j in range(n):
        to[i+1][j] = to[i][to[i][j]]

  v = 0
  for i in range(D-1, -1, -1):
    l = 1<<i # Look go to 2^i
    if l <= k:
        v = to[i][v]
        k -= l

  print(v+1)
    
main()

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
A = list(map(int, input().split()))

D = 60 #10**18は60桁なので2の59乗まで見る
MAX_N = 200005 #頂点番号
to = [[0 for _ in range(MAX_N)] for _ in range(D)]

#to[i][j]:jから2^i個先の頂点
for i in range(n):
    to[0][i] = A[i]
    to[0][i] -= 1

#ダブリングの表
for i in range(D-1):
    for j in range(n):
        to[i+1][j] = to[i][to[i][j]]

v = 0
for i in range(D-1, -1, -1):
    l = 1<<i #2^i個先を見る
    if l <= k:
        v = to[i][v]
        k -= l

print(v+1)

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

D = 60 #10**18は60桁なので2の59乗まで見る
MAX_N = 2*10**5+5 #頂点番号
to = [[0 for _ in range(D)] for _ in range(MAX_N)]

#to[i][j]:jから2^i個先の頂点
for i in range(n):
    to[0][i] = A[i]
    to[0][i] -= 1

#ダブリングの表
for i in range(D-1):
    for j in range(n):
        to[i+1][j] = to[i][to[i][j]]

v = 0
for i in range(D-1, -1, -1):
    l = 1<<i #2^i個先を見る
    if l <= k:
        v = to[i][v]
        k -= l

print(v+1)

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町はTrue
rec = [True] * (n+1)
idx = 1
#周期までループをまわす
while rec[idx]:
    rec[idx] = False
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = Town.index(idx)
#周期内
Cycl = len(Town) - Exce

if Cycl >= k:
    print(Town[k])
else:
    k -= Exce
    k %= Cycl
    print(Town[Exce+k])

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = Town.index(idx)
#周期内
Cycl = len(Town) - Exce

if Cycl >= k:
    print(Town[k])
else:
    k -= Exce
    k %= Cycl
    print(Town[Exce+k])

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#すべての町を訪れるまで
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

Exce = rec.index(idx)
Cycl = len(Town) - Exce

if Cycl > k:
    print(Town[k])
else:
    k -= Exce
    k %= Cycl
    print(Town[Exce+k])

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#すべての町を訪れるまで
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

Exce = rec[idx]
Cycl = len(Town) - Exce

if Cycl >= k:
    print(Town[k])
else:
    print(Town[Exce+(k-Exce)%Cycl])

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#すべての町を訪れるまで
while rec[idx] == -1:
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

Exce = rec[idx]
Cycl = len(Town) - Exce

if Cycl >= k:
    print(Town[k])
else:
    k -= Exce
    k %= Cycl
    print(Town[k+Exce])

Fixed submission:
n, k = map(int, input().split())
A = list(map(int, input().split()))

Town = []
#まだ訪れていない町は-1
rec = [-1] * (n+1)
idx = 1
#周期までループをまわす
while (rec[idx] == -1):
    rec[idx] = len(Town)
    Town.append(idx)
    idx = A[idx-1]

#周期前
Exce = rec[idx]
#周期内
Cycl = len(Town) - Exce

if Exce > k:
    print(Town[k])
else:
    Warp = (k - Exce) % Cycl
    print(Town[Exce+Warp])