Collaborative Problem-In this problem we consider two stacks A and B manipulated using the PushA(): Push element on stack A Push B(x): Push element r on stack B. MultiPopACk): Pop min(k,n) elements from A MultiPopBPop mla(, m) deneuts from B . Transfer(k): Repeatedly pop an element from A and push it on B, until either k elements have been moved or A is empty. Assume that A and B are implemented using doubly-linked lists such that Push.A and PushB, as well as a single pop from A or B, can be performed in O(1) time worst-case. (a) |5 pointsl What is the worst-case running time of the operations Multi PopA, MultiPopB and Transfer? (b) 125 points! Define a potential function (n, m) and use it to prove that the operations have amortized running time O(1)