Consider the following algorithm Precondition: A is a list Postcondition: If A has a majority element, Algorithml returns it. (Given a list A and an element e, we say that e is a majority element of A if and only if e occurs in A more than len(A)/2 times.) Algorithm2(A) 1. m = 0; e = None; 2. for i in range(len(A) If m = 0: 4 elif Aie: 6 7. else m=m-1; count 0; for j in range(len(A)): 10. 12. 13.if count > len(A)/2: 14 15 16 count- count +1 return e else return None (a) Give an appropriate loop invariant for the purpose of proving the partial correctness of the algo- (b) Use your loop invariant from part (a) to prove the partial correctness of Algorithm2 with respect (c) Prove your loop invariant rithm with respect to its given specification to the given specification