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

```python
import random

def tcgen():
    N = random.randint(1, 200000)
    K = random.randint(1, N + 1)
    return N, K

# Example usage:
if __name__ == "__main__":
    N, K = tcgen()
    print(N, K)
```

### Explanation:
1. **N Generation**:
   - `N` is generated randomly between 1 and 200,000 (inclusive), as per the constraints.

2. **K Generation**:
   - `K` is generated randomly between 1 and \(N + 1\) (inclusive), ensuring it adheres to the constraint \(1 \leq K \leq N + 1\).

### Sample Outputs:
- When you run the generator, it will give you random test cases within the specified constraints. For example:
  ```
  13795 4302
  200000 150000
  1 1
  ```

You can use this generator to create multiple test cases for your problem. The values will be printed in the required format for each test run.