Sure, I can help you write a test case generator for the Problem K: Chinol Choco. Here's the generator in Python:

```python
import random

def tcgen():
    # Generate values for n and m
    n = random.randint(2, 200)
    m = random.randint(1, 15)
    
    # Generate candidate locations for each store
    stores = []
    for _ in range(n):
        a, b = random.randint(0, 1000), random.randint(0, 1000)
        c, d = random.randint(0, 1000), random.randint(0, 1000)
        stores.append((a, b, c, d))
    
    # Generate locations for each factory
    factories = []
    for _ in range(m):
        x, y = random.randint(0, 1000), random.randint(0, 1000)
        factories.append((x, y))

    # Format the input as a string
    input_str = f"{n} {m}\n"
    for store in stores:
        input_str += f"{store[0]} {store[1]} {store[2]} {store[3]}\n"
    for factory in factories:
        input_str += f"{factory[0]} {factory[1]}\n"
    
    return input_str

# Example of generating a test case
print(tcgen())
```

### Explanation
- **n and m**: The generator first randomly selects the number of stores \( n \) and the number of factories \( m \) within the specified limits.
- **Stores**: For each store, it generates two candidate coordinates \((a_i, b_i)\) and \((c_i, d_i)\) within the range \([0, 1000]\).
- **Factories**: For each factory, it generates coordinates \((x_i, y_i)\) within the range \([0, 1000]\).
- **Input Formatting**: The generated data is formatted into a string that matches the problem's input format, which can be used directly for testing.

Feel free to run the `tcgen` function to generate test cases for your problem. Adjust the ranges or constraints if necessary to suit your needs.