Sure! Below is a test case generator for the given "Circular Sugoroku" problem. This generator will create random valid inputs according to the problem's constraints.

```python
import random

def tcgen():
    # Number of squares N
    N = random.randint(1, 100000)
    
    # Values on each square a1, a2, ..., aN
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, A

# Example usage:
N, A = tcgen()
print(N)
print(" ".join(map(str, A)))
```

This function generates:
- `N`: A random integer between 1 and 100000, inclusive.
- `A`: A list of `N` integers, each between 1 and 10^9, inclusive.

### Explanation:
1. **N**: The number of squares in the sugoroku board is generated randomly within the specified range (1 to 100000).
2. **A**: The list comprehension generates `N` integers where each integer is randomly chosen within the range 1 to 10^9.

### Example Output:
The output of running the `tcgen()` function might look like:
```
5
123456789 987654321 123456789 987654321 123456789
```

This can be directly used as input for the problem statement.

### Additional Notes:
- This generator creates a wide variety of test cases, including edge cases where `N` is at its minimum or maximum value.
- Each generated test case adheres to the constraints provided in the problem statement.