What is the story behind the nutcracker by Tchaikovsky in short?

A young girl is given a Nutcracker shaped like a soldier for Christmas. Her brother plays with it until it breaks. The girl bandages it and it turns into a prince. The rats, led by their king, attack. The prince and toy soldiers defeat the rats when the girl kills the king with her slipper. The prince and the girl fly to the Kingdom of Sweets, where there is much dancing and merrymaking.