|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|4 초||512 MB||1||1||1||100.000%|
Consider the following boring game about removing nodes from a forest. Initially, the forest contains only one tree with $N$ nodes, and your initial score is $0$. The game then goes as follows:
Please calculate the expected value of your final score multiplied by $N!$, modulo $10^9+7$.
The first line of input contains one integer $N$ indicating the number of nodes in the initial tree.
Each of the following $N-1$ lines contains two integers $x$ and $y$, indicating that $x$-th node and $y$-th node are connected by an edge in the given tree. The nodes are numbered from $1$ to $N$.
Output one number: the expected value of the final score of this boring game multiplied by $N!$, modulo $10^9+7$.
2 1 2
3 1 2 2 3