(Prove or disprove) The conjecture is that both NineTailModel and WeightedNineTailModel result in the same shortest path

 (Prove or disprove) The conjecture is that both NineTailModel and WeightedNineTailModel result in the same shortest path. Write a program to prove or disprove it. (Hint: Let tree1 and tree2 denote the trees rooted at node 511 obtained from NineTailModel and WeightedNineTailModel, respectively. If the depth of a node u is the same in tree1 and in tree2, the length of the path from u to the target is the same.)