Suppose we have a counter that stores an arbitrary number of bits and counts in binary. It always begin at 0. The only mutator operation it can perform is to increment, adding one to the current count. This changes one or more bits. Show that if we start at 0 and perform k increment operations, a total of O(k) bits will change. Hint 1: If you are stuck, count to 20 in binary on paper. After each increment, write how many bits have changed. See if you notice a pattern. Hint 2: Whenever you add one, give it some credit, similar to the analysis of expansion in lecture 7.