A tree is an undirected connected graph without cycles.

You are given a tree of $$$n$$$ vertices. Find the number of ways to choose exactly $$$k$$$ vertices in this tree (i. e. a $$$k$$$-element subset of vertices) so that all pairwise distances between the selected vertices are equal (in other words, there exists an integer $$$c$$$ such that for all $$$u, v$$$ ($$$u \ne v$$$, $$$u, v$$$ are in selected vertices) $$$d_{u,v}=c$$$, where $$$d_{u,v}$$$ is the distance from $$$u$$$ to $$$v$$$).

Since the answer may be very large, you need to output it modulo $$$10^9 + 7$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow.

Each test case is preceded by an empty line.

Each test case consists of several lines. The first line of the test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le k \le n \le 100$$$) — the number of vertices in the tree and the number of vertices to be selected, respectively. Then $$$n - 1$$$ lines follow, each of them contains two integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \neq v$$$) which describe a pair of vertices connected by an edge. It is guaranteed that the given graph is a tree and has no loops or multiple edges.

Output

For each test case output in a separate line a single integer — the number of ways to select exactly $$$k$$$ vertices so that for all pairs of selected vertices the distances between the vertices in the pairs are equal, modulo $$$10^9 + 7$$$ (in other words, print the remainder when divided by $$$1000000007$$$).

Equidistant Vertices

Examples