(10 points) Amortization You are given an m-bit binary counter, where the rightmost bit is the " 1 's" digit, the next bit is the "2's" digit, the next bit is the "4's" digit, and so on, up to the "2 2m1 's" digit. The function increment adds 1 to the counter, carrying when appropriate. Assuming that the counter starts at 0 , prove that increment takes O(1) amortized time. In other words, show that after n operations, the total amount of time spent is O(n). For simplicity, assume that the only operation that takes any time is flipping a bit in the counter