Please provide detailed step-by-step solutions! Will give thumb-up for a good answer. Thank you!

2. Suppose we perform a sequence of n operations on a data structure such that if some condition C(k) holds then the kth operation takes O(k) time, but otherwise it only takes O(1) time. For each condition C(k) listed below, determine the total time T(n) for the sequence of all n operations, and also the amortized time Tamortized(n) per each operation. a) IfC(k) is "k is a power of 2" then T(n):0n43) and Tamortized(n)=0(n1/3). b) If C(k) is "k is a power of 2" then T(n)-0(n) and Tamortized(n)-0(1) c) IfCk) is "k is a multiple of 2" then T(n)-On32) and Tamortizedn)-O(n2). 1/2 d If Ck) is "k is a multiple of 3" then T)-32 and Tamortized(n)-0 1:2