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 ≤ k ≤ n - 1, they're going to investigate all labeled trees with n vertices that share exactly k edges with Will's tree. Two labeled trees are different if and only if there's a pair of vertices (v, u) such that there's an edge between v and u in one tree and not in the other one.

Hopper and Joyce want to know how much work they have to do, so they asked you to tell them the number of labeled trees with n vertices that share exactly k edges with Will's tree, for each k. The answer could be very large, so they only asked you to tell them the answers modulo 1000000007 = 109 + 7.

威尔与颠倒世界的怪物之间存在着一种心灵感应，因此怪物所知道的一切，威尔也都知道。突然间，他开始不停地画画，一页又一页。他的母亲乔伊斯和霍珀警长将这些画作拼接在一起，发现这是一棵带标号的树！

树是一个连通且无环的图。威尔的树有 $n$ 个顶点。乔伊斯和霍珀并不理解这意味着什么，因此他们正在调查这棵树以及与其相似的树。对于每个满足 $0 \leq k \leq n-1$ 的 $k$，他们将调查所有具有 $n$ 个顶点的带标号树中，恰好与威尔的树共享 $k$ 条边的那些树。当且仅当存在一对顶点 $(v, u)$，使得在其中一棵树中 $v$ 与 $u$ 之间有边、而在另一棵树中没有该边时，这两棵带标号树才被认为是不同的。

霍珀和乔伊斯想知道他们需要完成多少工作，因此请你们计算：对每个 $k$，恰好与威尔的树共享 $k$ 条边的 $n$ 个顶点的带标号树的数目。答案可能非常大，因此只需输出结果对 $1000000007 = 10^9 + 7$ 取模后的值。

The first line of input contains a single integer n (2 ≤ n ≤ 100) — the size of the tree.

The next n - 1 lines contain the edges of Will's tree. Each line contains two integers v and u (1 ≤ v, u ≤ n, v ≠ u), endpoints of an edge. It is guaranteed that the given graph is a tree.

输入的第一行包含一个整数 $n$（$2 \leq n \leq 100$）——树的大小。

接下来的 $n-1$ 行包含 Will 的树的边。每行包含两个整数 $v$ 和 $u$（$1 \leq v, u \leq n$，$v \neq u$），表示一条边的两个端点。保证给定的图是一棵树。

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 1000 000 007 = 109 + 7.

在同一行中输出 $ n $ 个整数。其中第 $ i $ 个整数应为：与 Will 的树恰好共享 $ i-1 $ 条边的、含 $ n $ 个顶点的带标号树的数目，对 $ 1000,000,007 = 10^9 + 7 $ 取模的结果。