Suppose T is a binary tree that stores an integer key value in each node. Assume the following notation/operations on a binary tree the key T.key is the root node's integer key value the left child T.left is T's left subtree, which is possibly an empty tree (or null) the right child T.right is T's right subtree, which is possibly an empty tree (or null) (a) Write an efficient algorithm FINDMAXPRODUCT (T) in pseudocode that returns the max- imum product of the key values on all possible paths in the tree T, which is passed as the input to the function For the tree below, your algorithm should return a value of 240 (from the path with key values 5 -2 34-2 ) 3 -2 0 2 You must include appropriate comments in your pseudocode. (b) Trace the output of your algorithm 'running' using the binary tree shown above. You may wish to include a table of node values and corresponding 'temp' values generated at each nod e as your algorithm proceeds