Each of 2010 boxes in a line contains a single red marble, and for 1 \leq k \leq 2010, the box in the k^{\text {th }} position also contains k white marbles. Isabella begins at the first box and successively draws a single marble at random from each box, in order. She stops when she first draws a red marble. Let P(n) be the probability that Isabella stops after drawing exactly n marbles. What is the smallest value of n for which P(n)<\dfrac{1}{2010} ?
Answer Choices
A. 45
B. 63
C. 64
D. 201
E. 1005