You are given the graph shown below, and the heuristics functions h. You start from State S, and your goal is to go to State G. Find non-negative edge weights, x,y,z, and w, such that the graph satisfies each of the scenarios: Heuristic h(S)=20h(A)=2h(B)=15 a. Scenario 1: (3 points) Both greedy search and A find the optimal solution. x: y: Z: w: b. Scenario 2: (3 points) A search finds the optimal solution, but greedy search doesn't. X: y: z: w