Sure, I can write a test case generator for the given problem statement "Vector II". Here's the code for generating random test cases:

```python
import random

def tcgen():
    # Number of dynamic arrays
    n = random.randint(1, 1000)
    
    # Number of queries
    q = random.randint(1, 500000)
    
    queries = []
    
    for _ in range(q):
        operation = random.choice([0, 1, 2])
        t = random.randint(0, n-1)
        if operation == 0:
            # pushBack operation
            x = random.randint(-1000000000, 1000000000)
            queries.append(f"0 {t} {x}")
        elif operation == 1:
            # dump operation
            queries.append(f"1 {t}")
        elif operation == 2:
            # clear operation
            queries.append(f"2 {t}")
    
    # Combine n, q and queries into the final input format
    input_data = f"{n} {q}\n" + "\n".join(queries)
    
    return input_data

# Generate a test case and print it
print(tcgen())
```

This script generates a random test case for the "Vector II" problem. It randomly chooses the values for \( n \) and \( q \), and then generates a list of \( q \) queries. The queries are randomly selected among the three operations: `pushBack`, `dump`, and `clear`. The generated test case is formatted as specified in the problem statement. 

Here’s a breakdown of the code:
1. **Initialization**: Randomly determine the number of dynamic arrays \( n \) and the number of queries \( q \) within the specified constraints.
2. **Query Generation**:
   - For each query, randomly choose an operation among `pushBack`, `dump`, and `clear`.
   - Generate the required parameters for each operation:
     - `pushBack` requires an array index \( t \) and a value \( x \).
     - `dump` and `clear` only require an array index \( t \).
3. **Formatting**: Combine \( n \), \( q \), and the list of queries into the final input format and return it.

You can run this script to generate multiple test cases and use them for testing your competitive programming solution.