Sure, I can help you write a test case generator for the "Sliding Minimum Element" problem. Below is a Python function to generate random test cases for this problem:

```python
import random

def tcgen():
    N = random.randint(1, 10**6)
    L = random.randint(1, N)
    
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, L, A

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

### Explanation:

1. **N (number of elements)**: The function uses `random.randint(1, 10**6)` to generate a random integer between 1 and 1,000,000 (inclusive) for the number of elements in the array.
   
2. **L (size of sub-arrays)**: The function ensures that the size of the sub-arrays is at most `N` by generating a random integer between 1 and `N`.

3. **A (array elements)**: The function generates an array `A` of size `N` with random integers, each between 1 and 1,000,000,000 (inclusive).

### Example Usage:

```python
N, L, A = tcgen()
print(N, L)
print(" ".join(map(str, A)))
```

This code snippet will generate a random test case and print it in the format specified in the problem statement.

### Note:
Due to the constraints (with `N` up to 10^6 and `a_i` up to 10^9), the generated test cases can be quite large. If you want to test the generator for smaller values or specific scenarios, you can adjust the ranges accordingly. For example, you can set `N = random.randint(1, 100)` for smaller arrays during testing.