Downfall of 2041

Hello everyone, and welcome to my first post, as I have said, this is my first one, so dont comment/message me if its bad please, but lets get on

In this scenario, WW2 starts in 2035, the war goes hot early, and both sides drop nuclear bombs on each other, which results in that most of the human population dies out in 2041, which is the time they where dropped, most of the population of the world is now centered in Greenland and the Svalbards, there are also a significant amount of people in Africa, and 77 survivors in the forests of Hungary, the overall human population is ~70000 people, technologywise the world falls back to the technology of the middle ages, between 2085-2150, the humanity quickly recovers its technology and it is now back to that of the 19th century, and in 2251 (which is the last date in this scenario), humans rediscover electricity as they reach China