Indicate for each pair of expressions $(A, B)$ in the table below, whether $A$ is $O$, $o$, $\Omega$, $\omega$, or $\Theta$ of $B$. Assume that $k \geq 1$, $\epsilon > 0$, and $c > 1$ are constants. Your answer should be in the form of the table with "yes" or "no" written in each box.

A | B | $O$ | $o$ | $\Omega$ | $\omega$ | $\Theta$ |
---|---|---|---|---|---|---|

$\lg^kn$ | $n^\epsilon$ | yes | yes | no | no | no |

$n^k$ | $c^n$ | yes | yes | no | no | no |

$\sqrt{n}$ | $n^{\sin{n}}$ | no | no | no | no | no |

$2^n$ | $2^{n/2}$ | no | no | yes | yes | no |

$n^{\lg{c}}$ | $c^{\lg{n}}$ | yes | no | yes | no | yes |

$\lg(n!)$ | $\lg(n^n)$ | yes | no | yes | no | yes |