Recursive Digit Sum

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    You can solve this mathematically in Python with:

    result = (int(n) * int(k)) % 9
    return result if result != 0 else 9
    

    However, if n is a very long number, int(n) may raise a ValueError due to the digit limit introduced in recent Python versions. You can bypass this by increasing the limit:

    import sys
    sys.set_int_max_str_digits(100000)
    

    Use with caution, especially when handling untrusted input, as increasing the limit can expose your code to denial-of-service risks.

    Reference: Python Docs – Integer string conversion length limitation