The Big Cat and his Kitty (слэш)

Harrymort Prompt Friday 02 February – You know all these fics where either Harry or Voldemort get turned into a cat and the human takes care of the cat and they fall in love? Let's try something like that, but a little bit more different.
Harry and Voldemort both get turned into cats almost at the same time, in different circumstances. They run away in order not to be found by the others, and they end up meeting.
They go on talking about their problems and helping each other, without knowing who the other cat is, and finally find a solution.
They both re-transform at the same time.
How will they react to the fact that the most helpful, understanding person the world is actually your mortal enemy?
Please write more than 2000 words, if possible. Thank you!
Cover by RiddleSnape(AO3)/@S1L6Moon9(WP)