Bug Byte 2.0

Fill in the edge weights in the graph below with the numbers 1 through 25, using each number exactly once. Labeled nodes provide some additional constraints:

The sum of all edges directly connected to this node is B.

The product of all edges directly connected to this node is U.

There exists a non-self-intersecting path starting from this node where G is the sum of the weights of the edges on that path.

Once the graph is filled, start at the node with the second lowest edge sum and use the following greedy algorithm: At each juncture, take the highest weight edge that has not yet been traversed. Then, convert each edge along that path to a letter (1=A, 2=B, etc.) to find a secret message.