6. A car starts from point $A$ and drives to point $B$ (no reverse driving allowed), the distance between $A$ and $B$ is 2007. Some stations are set up along the way, with stations established at all points where the distance to $A$ is a multiple of 100 (the set of these stations is denoted as $X$), and stations established at all points where the distance to $A$ is a multiple of 223 (the set of these stations is denoted as $Y$). Each time the car stops during the journey, it either stops at the nearest station in set $X$ or the nearest station in set $Y$. The number of all possible stopping ways from $A$ to $B$ is $n$, which falls in the interval ( ).
(A) $[1,2007]$
(B) $[2008,20070]$
(C) $[20071,200700]$
(D) $[200701,+\infty)$
6. C.

Let $k$ represent the station that is $k$ units away from $A$, to 223 there are 3 ways, to $300, 400$ there are 4 ways each, to 446 there are 11 ways, to 500, 600 there are 15 ways each, to 669 there are 41 ways, to 700, 800 there are 56 ways each, to 892 there are 153 ways, to $900, 1000, 1100$ there are 209 ways each, to 1115 there are 780 ways, to $1200, 1300$ there are 989 ways each, to 1338 there are 2758 ways, to $1400, 1500$ there are 3747 ways each, to 1561 there are 10252 ways, to 1600, 1700 there are 13999 ways each, to 1784 there are 38250 ways, to $1800, 1900, 2000$ there are 52249 ways each, to 2007 there are 194997 ways.