Let k be a positive integer. Bernardo and Silvia take turns writing and erasing numbers on a blackboard as follows: Bernardo starts by writing the smallest perfect square with k+1 digits. Every time Bernardo writes a number, Silvia erases the last k digits of it. Bernardo then writes the next perfect square, Silvia erases the last k digits of it, and this process continues until the last two numbers that remain on the board differ by at least 2 . Let f(k) be the smallest positive integer not written on the board. For example, if k=1, then the numbers that Bernardo writes are 16,25,36,49, and 64 , and the numbers showing on the board after Silvia erases are 1,2,3,4, and 6 , and thus f(1)=5. What is the sum of the digits of f(2)+f(4)+f(6)+\cdots+f(2016) ?
Answer Choices
A. 7986
B. 8002
C. 8030
D. 8048
E. 8064