The set A=\{1,2,3,\dots,2044,2045\} contains 2045 elements. A subset S of A is called triple-free if no element of S equals three times another element of S. For example, \{1,2,4,5,10,2043\} is triple-free, but \{1,2,4,5,10,681,2043\} is not triple-free. The triple-free subsets of A that contain the largest number of elements contain exactly 1535 elements. There are n triple-free subsets of A that contain exactly 1535 elements. The integer n can be written in the form p^aq^b, where p and q are distinct prime numbers and a and b are positive integers. If N=p^2+q^2+a^2+b^2, then the last three digits of N are
Answer Choices
A. 202
B. 102
C. 302
D. 402
E. 502