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 ai and bi.
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.