Sum of Tree Path Weights

You are given a tree with N vertices and N - 1 edges. In a tree, there is exactly one simple path between any two distinct vertices.

Each edge has a non-negative integer weight. The weight of a path is defined as the product of the weights of all edges on that path. The weight of the tree is the sum of the weights of all paths connecting pairs of distinct vertices.

Given the tree, compute its weight.

The first line contains the number of vertices N. (1 <= N <= 100,000)

Each of the next N - 1 lines contains three integers A B W. This means vertices A and B are connected by an edge with weight W. (1 <= A, B <= N, 0 <= W <= 1,000)

Print the weight of the tree modulo 1,000,000,007.