If algorithm $A$ and another algorithm $B$ take $\log_2 (n)$ and $\sqrt{n}$ microseconds, respectively, to solve a problem, then the largest size $n$ of a problem these algorithms can solve, respectively, in one second are ______ and ______.
- $2^{10^n}$ and $10^6$
- $2^{10^n}$ and $10^{12}$
- $2^{10^n}$ and $6.10^6$
- $2^{10^n}$ and $6.10^{12}$