## TREESUM - Tree Sum

Let Lx denote the level of a node x in a rooted tree. Lx is 1 if x is the root, otherwise Lx = 1 + Ly, where y is the parent of x in the rooted tree.

You need to calculate the sum Lx ^ K for all nodes x in the tree.

### Input

The first line contains the number of test cases T. T test cases follow. The first line of each test case contains N and K, where N is the number of nodes in the tree. The following N - 1 lines contain two integers ai and bi, indicating an edge between nodes ai and bi in the tree. There is a blank line after each test case.

### Output

Output N lines for each test case. The i-th line should contain the required sum if the tree is rooted at node i. Output all values modulo 1000000007. Output a blank line after each test case.

### Example

```Sample Input:
2
3 2
0 1
1 2

3 3
0 1
0 2

Sample Output:
14
9
14

17
36
36```

### Constraints

1 <= T <= 10
1 <= N <= 20000
1 <= K <= 20
0 <= ai, bi < N

 Added by: Varun Jalan Date: 2010-09-20 Time limit: 1.570s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: C-CLANG C C++ 4.3.2 CPP CPP14 CPP14-CLANG C99 JAVA PYTHON PYTHON3 SWIFT Resource: own problem, used for Al Khwarizm '10