Hi, I'm Korean. '병'(byeong) depends on context, but you don't have to struggle to figure out the meaning of '병'. Because it's so different between bottle and pain. Nobody says "painless bottle" or "A bottle that doesn't feel pain"
Since 고통 and 없다 are two separate words, there should be a space between them. I just made a new exercise with the spacing issue fixed and thus I am locking this discussion. We are sorry for the confusion.