AMC 12A 2004 Problem 17

Let f be a function with the following properties:
(i) f(1)=1, and

(ii) f(2 n)=n \cdot f(n) for any positive integer n.

What is the value of f\left(2^{100}\right) ?

Answer Choices
A. 1
B. 2^{99}
C. 2^{100}
D. 2^{4950}
E. 2^{9999}