The line y=\tfrac{1}{3}x+1 divides the square region defined by 0\le x\le 2 and 0\le y\le 2 into an upper and a lower region. The line x=a divides the lower region into two regions of equal area. Then a can be written as \sqrt{s}-t, where s and t are positive integers. What is s+t?
Answer Choices:
A. 18
B. 19
C. 20
D. 21
E. 22