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

f_dict = {
  0: 1
}
def f(n):
  if f_dict.get(n):
    return f_dict.get(n)
  return (3 + f(n-1) * 2)


patty_dict = {
  0: 1
}
def total_patty(n):
  if patty_dict.get(n):
    return patty_dict.get(n)
  return (1 + 2 * total_patty(n - 1))

def count_patty(n, x):
  if x == 0:
    return 0
  elif 1 <= x and x <= f(n - 1) + 1:
    return count_patty(n - 1, x - 1)
  elif x == f(n - 1) + 2:
    return total_patty(n - 1) + 1
  elif f(n - 1) + 2 <= x and x <= 2 * f(n - 1) + 2:
    return total_patty(n - 1) + 1 + count_patty(n - 1, x - f(n - 1) - 2)
  else:
    return total_patty(n)

print(count_patty(n, x))

Fixed submission:
n, x = map(int, input().split())

f_dict = {
  0: 1
}
def f(n):
  if f_dict.get(n):
    return f_dict.get(n)
  return (3 + f(n-1) * 2)


patty_dict = {
  0: 1
}
def total_patty(n):
  if patty_dict.get(n):
    return patty_dict.get(n)
  return (1 + 2 * total_patty(n - 1))

def count_patty(n, x):
  if n == 0 and x == 1:
    return 1
  elif x == 0:
    return 0
  elif 1 <= x and x <= f(n - 1) + 1:
    return count_patty(n - 1, x - 1)
  elif x == f(n - 1) + 2:
    return total_patty(n - 1) + 1
  elif f(n - 1) + 2 <= x and x <= 2 * f(n - 1) + 2:
    return total_patty(n - 1) + 1 + count_patty(n - 1, x - f(n - 1) - 2)
  else:
    return total_patty(n)

print(count_patty(n, x))

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

f_dict = {
  0: 1
}
def f(n):
  if f_dict.get(n):
    return f_dict.get(n)
  return (3 + f(n-1) * 2)


patty_dict = {
  0: 1
}
def total_patty(n):
  if patty_dict.get(n):
    return patty_dict.get(n)
  return (1 + 2 * total_patty(n - 1))

def count_patty(n, x):
  if x == 0:
    return 0
  elif 1 <= x and x <= f(n - 1) + 1:
    return count_patty(n - 1, x - 1)
  elif x == f(n - 1) + 2:
    return total_patty(n - 1) + 1
  elif f(n - 1) + 2 <= x and x <= 2 * f(n - 1) + 2:
    return total_patty(n - 1) + 1 + count_patty(n - 1, x - f(n - 1) - 2)
  else:
    return total_patty(n)

print(count_patty(n, x))

Fixed submission:
n, x = map(int, input().split())

f_dict = {
  0: 1
}
def f(n):
  if f_dict.get(n):
    return f_dict.get(n)
  return (3 + f(n-1) * 2)


patty_dict = {
  0: 1
}
def total_patty(n):
  if patty_dict.get(n):
    return patty_dict.get(n)
  return (1 + 2 * total_patty(n - 1))

def count_patty(n, x):
  if n == 0 and x == 1:
    return 1
  elif x == 0:
    return 0
  elif 1 <= x and x <= f(n - 1) + 1:
    return count_patty(n - 1, x - 1)
  elif x == f(n - 1) + 2:
    return total_patty(n - 1) + 1
  elif f(n - 1) + 2 <= x and x <= 2 * f(n - 1) + 2:
    return total_patty(n - 1) + 1 + count_patty(n - 1, x - f(n - 1) - 2)
  else:
    return total_patty(n)

print(count_patty(n, x))

Buggy python submission (verdict: Time Limit Exceeded):
n, x = map(int, input().split())
hamburger_dict = {
  0: 'p'
}

def hamburger(n):
  if hamburger_dict.get(n):
    return hamburger_dict.get(n)
  return 'b' + hamburger(n - 1) + 'p' + hamburger(n - 1) + 'b'

print(hamburger(n)[0:x].count('p'))

Fixed submission:
n, x = map(int, input().split())

f_dict = {
  0: 1
}
def f(n):
  if f_dict.get(n):
    return f_dict.get(n)
  return (3 + f(n-1) * 2)


patty_dict = {
  0: 1
}
def total_patty(n):
  if patty_dict.get(n):
    return patty_dict.get(n)
  return (1 + 2 * total_patty(n - 1))

def count_patty(n, x):
  if n == 0 and x == 1:
    return 1
  elif x == 0:
    return 0
  elif 1 <= x and x <= f(n - 1) + 1:
    return count_patty(n - 1, x - 1)
  elif x == f(n - 1) + 2:
    return total_patty(n - 1) + 1
  elif f(n - 1) + 2 <= x and x <= 2 * f(n - 1) + 2:
    return total_patty(n - 1) + 1 + count_patty(n - 1, x - f(n - 1) - 2)
  else:
    return total_patty(n)

print(count_patty(n, x))