Bug Byte

Fill in the edge weights in the graph below with the numbers 1 through 24, using each number exactly once. Labeled nodes provide some additional constraints:

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

There exists a non-self-intersecting path starting from this node where N is the sum of the weights of the edges on that path. Multiple numbers indicate multiple paths that may overlap.

Once the graph is filled, find the shortest (weighted) path from to and convert it to letters (1=A, 2=B, etc.) to find a secret message.