SP8980 KOICOST - Cost

You are given an undirected graph with N verticies and M edges, where the weights are unique. There is a function Cost(u, v), which is defined as follows: While there is a path between vertex u and v, delete the edge with the smallest weight. Cost(u,v) is the sum of the weights of the edges that were deleted in this process.  For example, from the graph above (same as the sample input), Cost(2,6) is 2+3+4+5+6 = 20. Given an undirected graph, your task is to calculate the sum of Cost(u,v) for all vertices u and v, where u < v. Since the answer can get large, output the answer modulo 10^9.

The first line of the input consists of two integers, N and M. (1

Output the sum specified in the problem statement.