$5)$ Consider the UCT search tree shown below.

a$)$ Determine which leaf node would be expanded for a value of $\backslash (\backslash$mathrm$\{$c$\}=1\backslash ).$ Show your calculations of Q$*$ for each step.

b$)$ Show the new tree after running a simulation using a random policy rollout from this leaf node, assuming the payoff value at the end is a $0.$ Make sure to update the values within the existing nodes to account for this additional simulation result and add the new node to the tree.