Sure! Let's write a test case generator for the given problem statement. The generator will create random values for \(K\), \(A\), and \(B\) within the specified constraints.

Here is the test case generator:

```python
import random

def tcgen():
    K = random.randint(1, 10**9)
    A = random.randint(1, 10**9)
    B = random.randint(1, 10**9)
    
    return K, A, B

# Example usage:
K, A, B = tcgen()
print(K, A, B)
```

This generator will produce random values for \(K\), \(A\), and \(B\), ensuring they are within the given constraints (1 ≤ \(K, A, B\) ≤ 10^9).

### Explanation:
1. **K**: The number of operations, randomly chosen between 1 and 10^9.
2. **A**: The number of biscuits required to exchange for 1 yen, randomly chosen between 1 and 10^9.
3. **B**: The number of biscuits you get for 1 yen, randomly chosen between 1 and 10^9.

The generator can be used to produce a variety of test cases to thoroughly test the solution for the given problem statement.