Suppose that 13 cards numbered 1,2,3, \ldots, 13 are arranged in a row. The task is to pick them up in numerically increasing order, working repeatedly from left to right. In the example below, cards 1,2,3 are picked up on the first pass, 4 and 5 on the second pass, 6 on the third pass, 7,8,9,10 on the fourth pass, and 11,12,13 on the fifth pass. For how many of the 13 ! possible orderings of the cards will the 13 cards be picked up in exactly two passes?
Answer Choices
A. 4082
B. 4095
C. 4096
D. 8178
E. 8191