Problem Description

There is a tree,there is a life.Can you solve this problem about tree?
Here we have a tree which has n vertices.
We define dist(u, v) as the number of edges on the path from u to v.
And for each vertices u , define E_u =
Give you the tree and k.
Print E_i for every vertices(from 1 to n).(mod 10007 for convenience).

Input

The first line contains integer T(1  T  5),denote the number of the test cases.
For each test cases,the first line contains two integers n,k(1<=n<=50000, 1<=k<=500).
Then next n-1 lines,each lines contains two integer a,b(1<=a, b<=n),denote there is an edge between a, b.

Output

For each test cases,print n lines,the i-th line contains E_i.

1
5 3
1 2
2 3
3 4
4 5

100
37
18
37
100

Hint

Thank oimaster for this problem :).

Author

WJMZBMR