Suppose we wish not only to increment a counter of length mN but also to reset it to zero (i.e., make all bits in it 0). Counting the time to examine or modify a bit as (1), show how to implement INCREMENT and operations on a counter (represented as an array of bits) so that any sequence of n operations takes O(1) amortized time per operation. You may assume that the counter is initially zero and that you may access and modify any specific bit (say bit j[m] ) in O(1) time. Additionally, you may assume that the total count in the counter never exceeds 2m1 during the course of the n operations. Prove correctness and running time of your algorithms. (Hint: Keep a pointer to the highest-order 1.)