Sure! Let's create a test case generator for the given problem statement. The generator will create random valid inputs based on the given constraints.

Here's the generator:

```python
import random

def tcgen():
    # Generate a random integer N between 1 and 10^5 (inclusive)
    N = random.randint(1, 10**5)
    
    # Generate N integers each between 1 and 10^9 (inclusive)
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, A

# Example usage:
if __name__ == "__main__":
    N, A = tcgen()
    print(N)
    for a in A:
        print(a)
```

### Explanation:
1. **N**: It generates a random integer between 1 and \(10^5\) (inclusive). This represents the number of different colors of apples.
2. **A**: It generates a list of \(N\) integers, each between 1 and \(10^9\) (inclusive). Each integer \(A[i]\) represents the number of apples of color \(i+1\).

When you run the `tcgen()` function, it will print \(N\) and the list of integers \(A\) representing the number of apples of each color.

### Example Output:
Here’s an example of what the output might look like:
```
5
345
678
12345
67890
234567
```

This output means there are 5 different colors of apples, and the counts of apples for each color are 345, 678, 12345, 67890, and 234567, respectively.

You can use this generator to create various test cases for the problem, ensuring that the solution can handle a wide range of inputs.