Consider the following pseudocode for calculating ab (where a and b are positive integers)

FastPower(a,b) : if b = 1 return a else

c := a*a ans := FastPower(c,[b/2]) if b is odd return a*ans else return ans end

Here [x] denotes the floor function, that is, the largest integer less than or equal to x.

Now assuming that you use a calculator that supports multiplication and division (i.e., you can do multiplications and divisions in constant time), what would be the overall asymptotic running time of the above algorithm (as a function of b)?

A. O(b log (b))

B. O(b)

C. ?(b^(1/2))

D. O(log (b))