Construct the graph, now think for trees, you would find that setting any value x for a node satisfies the sum condition accordingly (lets forget the condition 1<=x<=k for now), Now if there is a cycle you would find similar thing for cycles of even length, but cycles of odd length has an unique x (for a node). So for each component check if it is bipartite or not, if it is not bipartite there can be at most 1 solution, otherwise you check the max and min value for all the white nodes and max and min for all the black nodes (initializing any of the node with 0) now set the (1 <= x <= k) condition for these corner points (max and min) and count the valid cases, this is done because if we increase the value of any black node by 1 then value of all the black nodes increases by 1 and all white nodes decreases by 1. So now you have a solution where the maxima is at most k, do the same for k = k-1 and subtract the result.

In the e-mail I received. Anyway, it turned out that "prizes worth $$$360$$$ dollars" means something like "$$$100$$$ Amazon coupons worth $$$3.60$$$ dollars".

Let's rename CodeRush to Yukiclone.