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

```python
import random

def tcgen():
    N = random.randint(1, 100)
    K = random.randint(1, N)
    return N, K

# Example usage:
if __name__ == "__main__":
    for _ in range(10):  # Generate 10 test cases as an example
        N, K = tcgen()
        print(f"{N} {K}")
```

### Explanation

- **N**: The number of balls is chosen randomly between 1 and 100 inclusive.
- **K**: The number of persons is chosen randomly between 1 and \(N\) inclusive.
  
This setup ensures that the constraints \(1 \leq K \leq N \leq 100\) are satisfied.

### How to Use

To use this test case generator, simply run the script. Each call to `tcgen()` will generate a new test case with values for \(N\) and \(K\) that can be used to test the solution for the given problem statement.

### Sample Output

Here is how the output might look when generating 10 test cases:

```
67 35
32 20
100 78
45 12
12 5
90 53
1 1
25 10
88 88
50 30
```

Each pair of numbers represents a test case with \(N\) balls and \(K\) persons.