The information below is about the corporate sector in India. % of total
| Category | Factories | Employment | Fixed Capital | Gross Output | Value Added |
|---|---|---|---|---|---|
| All PSUs | 7.0 | 27.2 | 43.2 | 25.8 | 30.8 |
| Central PSU | 1.0 | 10.5 | 17.5 | 12.7 | 14.1 |
| State & Local PSU | 5.2 | 16.2 | 24.3 | 11.6 | 14.9 |
| Central & State PSU | 0.8 | 1.0 | 1.4 | 1.5 | 1.8 |
| Joint Sector | 31.8 | 5.1 | 6.8 | 8.4 | 8.1 |
| Private Sector | 90.3 | 64.6 | 46.8 | 63.8 | 58.7 |
| Others | 0.9 | 2.6 | 3.2 | 2.0 | 2.4 |




| 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: