To generate test cases for this problem, we need to create cases that simulate the input format and ensure that they are within the given constraints. Here's a Python function that generates random test cases for this problem:

```python
import random

def generate_test_case():
    # Randomly generate A and B within the constraints
    A = random.randint(1, 10)
    B = random.randint(1, 10)
    
    # Generate the d matrix with random values between 1 and 100
    d_matrix = [[random.randint(1, 100) for _ in range(B)] for _ in range(A)]
    
    # Format the input as a string
    input_str = f"{A} {B}\n"
    for row in d_matrix:
        input_str += ' '.join(map(str, row)) + '\n'
    
    return input_str.strip()

# Example usage
for _ in range(5):  # Generate 5 test cases
    print(generate_test_case())
    print()
```

This function will create random test cases for the problem. Each test case includes:
1. Random values for \(A\) and \(B\) within the range [1, 10].
2. A matrix \(d_{x,y}\) with dimensions \(A \times B\), filled with random integers between 1 and 100.

### Explanation:
- **A and B**: The number of rows and columns of the matrix \(d_{x,y}\) are randomly selected within the allowed range [1, 10].
- **d_matrix**: The matrix is populated with random integers between 1 and 100.

This generated input can be directly used to test the implementation of the problem. Each test case is printed in the required format. You can adjust the number of test cases generated by changing the range in the `for` loop.