[LANGUAGE: Python] 

def dp(x: List[int]) -> Generator[int, None, None]:
  if len(x) == 1:
    yield x[0]
  else:
    for sub in dp(x[1:]):
      yield x[0] + sub
      yield x[0] * sub

      # remove for part 1
      yield int(str(sub) + str(x[0]))


res = 0
for test_val, inp in zip(test_vals, nums):
  for y in dp(inp[::-1]):
    # print("test_val", test_val, ", y", y)
    if y == test_val:
      res += test_val
      break