Consider the following problem setup: The head TA is figuring out the discussion schedule. We have M TAs and N discussion sections. Each discussion section has a known time slot, and fortunately, at most 2 discussions are in the same time slot. In the N discussion sections, we need exactly K of them to be e-prep sections, and the rest to be normal sections. We also want the following conditions to hold:• We would like to have exactly one TA for each discussion section.• A TA cannot be teaching 2 discussion at the same time slot.• Some TAs do not teach regular discussions, some do not teach e-prep, and others can teach either.• If two discussions are in the same time slot, we also don’t want them to be the same type of discussion for the sake of best allocation of resources.(a) Cast this as a search problem. Specifically, appropriately define the state representation, the successor function, the start state and the goal test. State representation:Successor function:Start state:Goal test:(b) Calculate the state space size and the branching factor of the search tree, then suggest a search algorithm to tackle the problem. If you are using DFS/BFS, explain your choice of algorithm in a paragraph. If you are using UCS/Greedy/A* search, please define in a paragraph what cost function and/or heuristic is being used. It doesn’t necessarily need to be a rigorous definition but more of a qualitative description of what the cost function/heuristic does. State space size:Branching factor:Proposed search algorithm:Explanation: