To generate test cases for the given problem, we'll need to simulate the inputs based on the constraints provided. Here is a Python function to generate test cases for the problem statement described:

```python
import random

def tcgen():
    # Generate N and D
    N = random.randint(1, 5 * 10**5)
    D = random.randint(1, 10**9)
    
    # Generate the list of distances d_i
    d = [random.randint(1, 10**9) for _ in range(N)]
    
    # Generate Q
    Q = random.randint(1, 5 * 10**5)
    
    # Generate the list of indices q_i
    q = [random.randint(1, N) for _ in range(Q)]
    
    return N, D, d, Q, q

# Example usage:
N, D, d, Q, q = tcgen()

# Printing the generated test case in the required format
print(N, D)
print(" ".join(map(str, d)))
print(Q)
print(" ".join(map(str, q)))
```

### Explanation:
1. **N**: Random integer between 1 and 500,000 (inclusive).
2. **D**: Random integer between 1 and 1,000,000,000 (inclusive).
3. **d**: List of N random integers, each between 1 and 1,000,000,000 (inclusive), representing the distances Alice inputs to the vehicle.
4. **Q**: Random integer between 1 and 500,000 (inclusive).
5. **q**: List of Q random integers, each between 1 and N (inclusive), representing the indices where the witch might rewrite a number.

This function generates a test case according to the constraints provided in the problem statement. The values are printed in the format that matches the problem's input specification.