Sure! Here is the test case generator for the provided problem statement:

```python
import random

def tcgen():
    # Generate N: 1 <= N <= 16
    N = random.randint(1, 16)
    
    # Generate M: 0 <= M <= 16
    M = random.randint(0, 16)
    
    # Generate A array: each A_i is distinct, sorted and within the range [2, 2^N]
    A = sorted(random.sample(range(2, 2**N + 1), M))
    
    return N, M, A

# Example usage:
if __name__ == "__main__":
    # Generate a single test case
    N, M, A = tcgen()
    print("N:", N)
    print("M:", M)
    print("A:", A)

    # You can generate multiple test cases by looping
    for _ in range(10):
        N, M, A = tcgen()
        print("Generated Test Case:")
        print("N:", N)
        print("M:", M)
        print("A:", A)
```

This generator ensures that the constraints are met:

1. \(N\) is between 1 and 16.
2. \(M\) is between 0 and 16.
3. The elements in array \(A\) are distinct, sorted, and within the range \([2, 2^N]\).

You can run the above code to generate test cases for the problem.