\frac {x_0} {y_0}=a_0+\frac 1 {a_1+\frac 1 {a_2+\frac 1 {...a_k+\frac 1 {2a_0+\frac 1 {a_1+\frac 1 {...a_{k-1}+\frac 1 {a_k}}}}}}}}}