The following is a function defined for all positive rational values of $x$.

$$f(x)=\{\begin{array}{ll}x& x\text{ is integral}\\ f(\frac{1}{1-x})& x<1\\ f(\frac{1}{\lceil x\rceil -x}-1+f(x-1))& \text{otherwise}\end{array}$$

For example, $f(3/2)=3$, $f(1/6)=65533$ and $f(13/10)=7625597484985$.

Find $f(22/7)$. Give your answer modulo ${10}^{15}$.