CF917D Stranger Trees

Will shares a psychic connection with the Upside Down Monster, so everything the monster knows, Will knows. Suddenly, he started drawing, page after page, non-stop. Joyce, his mom, and Chief Hopper put the drawings together, and they realized, it's a labeled tree! A tree is a connected acyclic graph. Will's tree has $ n $ vertices. Joyce and Hopper don't know what that means, so they're investigating this tree and similar trees. For each $ k $ such that $ 0

The first line of input contains a single integer $ n $ ( $ 2

Print $ n $ integers in one line. $ i $ -th integer should be the number of the number of labeled trees with $ n $ vertices that share exactly $ i-1 $ edges with Will's tree, modulo $ 1000000007=10^{9}+7 $ .