Sure! I can help you write a test case generator for the given problem. Here is the generator code in Python:

```python
import random

def tcgen():
    # Generate a random integer for N within the constraint
    N = random.randint(2, 200000)

    # Generate a random integer for K within the constraint
    K = random.randint(1, N-1)

    # Generate a list of N random integers for A within the constraint
    A = [random.randint(1, 10**9) for _ in range(N)]

    return N, K, A

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

# Example usage
N, K, A = tcgen()
print_test_case(N, K, A)
```

### Explanation:
1. **Constraints Handling**:
    - `N` is generated to be a random integer between 2 and 200000.
    - `K` is generated to be a random integer between 1 and N-1.
    - `A` is a list of `N` random integers, each between 1 and 1,000,000,000.

2. **Output Format**:
    - The test case is printed in the required format: 
        - First, it prints the integers `N` and `K`.
        - Then, it prints the list of `A` values.

You can use this generator to create random test cases for your problem and validate your solution against these generated test cases.