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

```python
import random

def tcgen():
    # Constraint values
    N_max = 10**5
    A_max = 10**9
    K_max = 10**9
    
    # Generate N
    N = random.randint(1, N_max)
    
    # Generate K
    K = random.randint(1, K_max)
    
    # Generate array A of size N with values between 1 and A_max
    A = [random.randint(1, A_max) for _ in range(N)]
    
    return N, K, A

# Function to print the test case in the required format
def format_test_case(N, K, A):
    print(N, K)
    print(' '.join(map(str, A)))

# Generate a test case
N, K, A = tcgen()

# Print the test case
format_test_case(N, K, A)
```

This code will generate a random valid test case for the given problem. The `tcgen` function generates values for \(N\), \(K\), and the array \(A\) based on the constraints provided. The `format_test_case` function prints the generated test case in the required input format.

Here is how you can use it:

1. Call `tcgen()` to generate a test case.
2. Use `format_test_case(N, K, A)` to print the generated test case.

Example usage:

```python
N, K, A = tcgen()
format_test_case(N, K, A)
```

It will print something like:

```
92345 987654321
123456789 987654321 123456789 987654321 ... (up to 92345 numbers)
```

This ensures that the test cases are generated within the constraints provided for the problem.