Answer the questions based on the following table.
| Period/ Product | Mumbai 1993-94 | Kolkata 1993-94 | Delhi 1993-94 | Chennai 1993-94 |
|---|---|---|---|---|
| HD | $20$–$15$ | $35$–$30$ | $20$–$15$ | $20$–$30$ |
| CO | $20$–$25$ | $30$–$15$ | $15$–$10$ | $20$–$15$ |
| BN | $45$–$40$ | $25$–$35$ | $35$–$35$ | $10$–$10$ |
| MT | $15$–$20$ | $10$–$20$ | $10$–$10$ | $50$–$45$ |




| A | B | C | D | Average |
|---|---|---|---|---|
| 3 | 4 | 4 | ? | 4 |
| 3 | ? | 5 | ? | 4 |
| ? | 3 | 3 | ? | 4 |
| ? | ? | ? | ? | 4.25 |
| 4 | 4 | 4 | 4.25 |
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: