write a go solution for Description:
You are given a tree G with n vertices and an integer k. The vertices of the tree are numbered from 1 to n.

For a vertex r and a subset S of vertices of G, such that |S|=k, we define f(r,S) as the size of the smallest rooted subtree containing all vertices in S when the tree is rooted at r. A set of vertices T is called a rooted subtree, if all the vertices in T are connected, and for each vertex in T, all its descendants belong to T.

You need to calculate the sum of f(r,S) over all possible distinct combinations of vertices r and subsets S, where |S|=k. Formally, compute the following: \sum_{r \in V} \sum_{S \subseteq V, |S| = k} f(r, S), where V is the set of vertices in G.

Output the answer modulo 10^9+7.

Input Format:
The first line contains two integers n and k (3<=n<=2*10^5, 1<=k<=n).

Each of the following n-1 lines contains two integers x and y (1<=x,y<=n), denoting an edge between vertex x and y.

It is guaranteed that the given edges form a tree.

Output Format:
Print the answer modulo 10^9+7.

Note:
The tree in the second example is given below:

We have 21 subsets of size 2 in the given tree. Hence, S \in \left\{\{1, 2\}, \{1, 3\}, \{1, 4\}, \{1, 5\}, \{1, 6\}, \{1, 7\}, \{2, 3\}, \{2, 4\}, \{2, 5\}, \{2, 6\}, \{2, 7\}, \{3, 4\}, \{3, 5\}, \{3, 6\}, \{3, 7\}, \{4, 5\}, \{4, 6\}, \{4, 7\}, \{5, 6\}, \{5, 7\}, \{6, 7\} \right\}. And since we have 7 vertices, 1<=r<=7. We need to find the sum of f(r,S) over all possible pairs of r and S.

Below we have listed the value of f(r,S) for some combinations of r and S.

- r=1, S=3,7. The value of f(r,S) is 5 and the corresponding subtree is 2,3,4,6,7.
- r=1, S=5,4. The value of f(r,S) is 7 and the corresponding subtree is 1,2,3,4,5,6,7.
- r=1, S=4,6. The value of f(r,S) is 3 and the corresponding subtree is 4,6,7.. Output only the code with no comments, explanation, or additional text.