There are $2009$ white balls and $2010$ black balls in the box. There are enough black balls outside the box. Take two balls out of the box at any time, and if they are of the same color, take one black ball and put it back into the box. If they are of different color, put one of the white balls back into the box. After doing this operation $4018$ times, how many balls are left in the box and what color are they? 
选项为:A:$1$, white  B:$2$, white  C:$1$, black  D:$2$, black  E:$3$,white  请回答其中一个选项.