Sure, here is a test case generator for the problem statement provided:

```python
import random

def tcgen():
    # Constraint limits
    N = random.randint(1, 20)
    A = random.randint(1, 50)
    B = random.randint(1, 50)
    
    return N, A, B

# Example usage:
for _ in range(5):  # Generate 5 test cases
    N, A, B = tcgen()
    print(f"{N} {A} {B}")
```

This generator will produce random test cases within the provided constraints. Each test case will consist of three integers \(N\), \(A\), and \(B\). The function `tcgen()` follows the constraints:
- \(1 \leq N \leq 20\)
- \(1 \leq A \leq 50\)
- \(1 \leq B \leq 50\)

Here are some sample outputs you might get when running the generator:

```
3 46 22
17 9 13
5 23 30
20 50 4
14 6 45
```