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def generate_list_using_two_numbers(input1: int, input2: int, output_array_length: int):
    # Extract digits from the two numbers
    digits1 = str(input1)
    digits2 = str(input2)

    # Create a set to store unique combinations of numbers
    unique_numbers = set()

    # Generate all possible combinations of the digits
    for d1 in digits1:
        for d2 in digits1:
            unique_numbers.add(int(d1 + d2))
        for d2 in digits2:
            unique_numbers.add(int(d1 + d2))
    
    for d1 in digits2:
        for d2 in digits1:
            unique_numbers.add(int(d1 + d2))
        for d2 in digits2:
            unique_numbers.add(int(d1 + d2))

    # Convert the set to a sorted list
    sorted_numbers = sorted(unique_numbers)

    # Return the first 'output_array_length' numbers
    return sorted_numbers[:output_array_length]

# Example usage
input1 = 12
input2 = 34
output_length = 10
result = generate_list_using_two_numbers(input1, input2, output_length)
print(result)