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

```python
import random

def tcgen():
    # Generate a random value for N in the range [1, 200000]
    N = random.randint(1, 2 * 10**5)
    # Generate a random value for K in the range [1, N+1]
    K = random.randint(1, N + 1)
    
    return N, K

# Function to print the generated test case in the required format
def print_test_case():
    N, K = tcgen()
    print(N, K)

# Example usage
print_test_case()
```

This `tcgen` function generates random values for \( N \) and \( K \) based on the given constraints:

1. \( N \) is randomly chosen between 1 and 200,000.
2. \( K \) is randomly chosen between 1 and \( N + 1 \).

The `print_test_case` function calls `tcgen` to generate a test case and prints it in the required format.

You can run `print_test_case()` multiple times to generate different test cases.