Creating a test case generator for the "K-th String" problem involves generating random values for \( N \), \( A \), \( K \), and a permutation of suffix array indices. Below is a Python function to generate test cases for this problem:

```python
import random

def tcgen():
    # Generate N within the given constraints
    N = random.randint(1, 10**5)
    
    # Generate A within the given constraints
    A = random.randint(1, 26)
    
    # Generate K within the given constraints
    K = random.randint(1, 10**18)
    
    # Generate a permutation of numbers from 1 to N for the suffix array
    SA = random.sample(range(1, N + 1), N)
    
    # Print the generated test case
    print(N, A, K)
    for sa in SA:
        print(sa)

# Example usage
tcgen()
```

### Explanation:
1. **Generating \( N \)**: 
   - \( N \) is an integer between 1 and \( 10^5 \). The function `random.randint(1, 10**5)` is used to generate this random value.

2. **Generating \( A \)**: 
   - \( A \) is an integer between 1 and 26. The function `random.randint(1, 26)` is used to generate this random value.

3. **Generating \( K \)**: 
   - \( K \) is a very large integer between 1 and \( 10^{18} \). The function `random.randint(1, 10**18)` is used to generate this random value.

4. **Generating Suffix Array (SA)**:
   - The suffix array is a permutation of numbers from 1 to \( N \). The function `random.sample(range(1, N + 1), N)` generates a random permutation of these numbers.

5. **Printing the Test Case**:
   - The generated values are printed in the required format.

You can use this generator function to create multiple test cases for testing purposes. Adjust the function if you need to generate test cases with specific properties or constraints.