A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:

A

$$17\frac{11}{17}$$ days

B

$$17\frac{11}{19}$$ days

C

$$14\frac{11}{17}$$ days

D

$$11\frac{11}{17}$$ days