Read the following cartoon carefully.

Study the following question carefully and choose the right answer.
Statement: Should articles of only deserving authors be allowed to be published?
Arguments: \[\begin{array}{|c|l|}\hline (I) & \text{No, it is not possible to draw a line between the deserving and the undeserving.} \\ \hline (II) & \text{Yes, it will save a lot of paper which is already in short supply.} \\ \hline \end{array}\]

For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: