Please design the data structure in pseudo code

We want to design a list-like data structure that supports the following operations on integers. ADDTOFRONT(e): Adds a new element e at the front of the list. ADDToBack(e): Adds a new element e at the end of the list. REMOVEFROMFRONT(): Removes the first element from the list and returns it. REMOVEFROMBACK(): Removes the last element from the list and returns it. SETELEMENT(i, e): Sets the element of the i-th element of the list to e. Each operation should run in O(1) time. You can assume that we know that the list will never contain more than k elements (k is not a constant and should not show up in your running time). Example execution: ADD TOBACK(0) [0] ADDTOFRONT(-1) (-1,0] ADD TO FRONT(2) [2,-1,0] SETELEMENT(1,6) [2,6,0] REMOVEFROMBACK() [2,6], returns o REMOVEFROMFRONT() [6], returns 2 a) Design a data structure that supports the above operations in the required time. b) Briefly argue the correctness of your data structure and operations. c) Analyse the running time of your operations