Sure! Here's a test case generator for the given problem statement:

```python
import random

def tcgen():
    N = random.randint(1, 16)  # N can be between 1 and 16
    M = random.randint(0, 16)  # M can be between 0 and 16
    max_value = 2**N
    
    A = sorted(random.sample(range(2, max_value + 1), M))
    
    return N, M, A

def format_input(N, M, A):
    input_str = f"{N} {M}\n"
    if M > 0:
        input_str += ' '.join(map(str, A)) + '\n'
    return input_str

def format_output(output):
    return f"{output}\n"

# Generate a test case
N, M, A = tcgen()
input_str = format_input(N, M, A)
print("Generated Input:")
print(input_str)

# Note: The output generation/verification requires solving the problem, which is not included here.
```

### Explanation
1. **Random Generation of N and M**: 
    - `N` is randomly chosen between 1 and 16, inclusive.
    - `M` is randomly chosen between 0 and 16, inclusive.
    
2. **Generate the List `A`**:
    - `A` is a sorted list containing `M` unique integers. These integers are sampled from the range `[2, 2^N]`.
    
3. **Formatting the Input**:
    - The function `format_input` converts `N`, `M`, and `A` into the required input format.
    
4. **Example Usage**:
    - The test case generator produces a test case input, which is printed.

### Note
- The generator produces inputs for the problem. To fully test the problem, you would also need a function to compute the expected output. This function would implement the logic to determine the number of permutations where Player 1 becomes the champion, considering the constraints and rules given in the problem statement.