Given a tree with $$$N$$$ vertices, find the number of rooted trees with $$$K$$$ vertices, including vertex 1. Constraints: $$$1 \leq K \leq N \leq 3000$$$.

Example :
Let $$$N$$$ = $$$5$$$ and the tree be this :

Then for K = 1, 2, 3, 4, 5 the solutions are :