Problem Statement

You are given a tree with N vertices and N-1 edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and b_i.
You have coloring materials of K colors.
For each vertex in the tree, you will choose one of the K colors to paint it, so that the following condition is satisfied:

• If the distance between two different vertices x and y is less than or equal to two, x and y have different colors.

How many ways are there to paint the tree? Find the count modulo 1\ 000\ 000\ 007.

What is tree?
A tree is a kind of graph. For detail, please see: Wikipedia "Tree (graph theory)"

What is distance?
The distance between two vertices x and y is the minimum number of edges one has to traverse to get from x to y.

Input

Input is given from Standard Input in the following format:
N K
a_1 b_1
a_2 b_2
.
.
.
a_{N-1} b_{N-1}

Output

Print the number of ways to paint the tree, modulo 1\ 000\ 000\ 007.

Constraints

• $1 \leq N,K \leq 10^5$
• $1 \leq a_i,b_i \leq N$
• The given graph is a tree.

Sample Input 1

4 3
1 2
2 3
3 4

Sample Output 1

6

There are six ways to paint the tree.

Sample Input 2

5 4
1 2
1 3
1 4
4 5

Sample Output 2

48

Sample Input 3

16 22
12 1
3 1
4 16
7 12
6 2
2 15
5 16
14 16
10 11
3 10
3 13
8 6
16 8
9 12
4 3

Sample Output 3

271414432

见题面 Input 部分

见题面 Output 部分