Tree land has n cities, connected by n−1 roads. You can go to any city from any city. In other words, this land is a tree. The city numbered one is the root of this tree.
There are n ministers numbered from 1 to n. You will send them to n cities, one city with one minister.
Since this is a rooted tree, each city is a root of a subtree and there are n subtrees. The leader of a subtree is the minister with maximal number in this subtree. As you can see, one minister can be the leader of several subtrees.
One day all the leaders attend a meet, you find that there are exactly k ministers. You want to know how many ways to send n ministers to each city so that there are k ministers attend the meet.
Give your answer mod 1000000007.
Multiple test cases. In the first line there is an integer T, indicating the number of test cases. For each test case, first line contains two numbers n,k. Next n−1 line describe the roads of tree land.
T=10,1≤n≤1000,1≤k≤n
For each test case, output one line. The output format is Case #x: ans, x is the case number,starting from 1.
2 3 2 1 2 1 3 10 8 2 1 3 2 4 1 5 3 6 1 7 3 8 7 9 7 10 6
Case #1: 4 Case #2: 316512