base2i

Write a function P4:

• Mr. Park ($(1+6i)$ years old) has two eyes, so he loves $2i$. He wants to advertise the base $2i$ system.

• In the base $2i$ system, each complex number has the following representation: [\cdots d_2d_1d_0.d_{-1}d_{-2}\cdots] which means [\cdots+d_2\cdot b^2+d_1\cdot b^1+d_0\cdot b^0+d_{-1}\cdot b^{-1}+d_{-2}\cdot b^{-2}+\cdots] where $b=2i$, and $d\_k\in\{0,1,2,3\}$ for each $k$.

• input parameter: two integers x, y satisfying $\max(|$x$|$,$|$y$|)\le10^6$

• return value: the string representing the complex number x$+i$y in the base $2i$ system, satisfying the followings:

  • Each character in the string is one of '0', '1', '2', '3', '.'.
  • The string contains exactly one '.'.
  • There is exactly one character after '.'.
  • The string does not start with '.'.
  • The string does not start with '0' if there are more than one character before '.'.

• For example, 31.0 is the base $2i$ representation of $1+6i$ since $1+6i=3\cdot(2i)^1+1\cdot(2i)^0+0\cdot(2i)^{-1}$