# Some large numbers again...

Number Theory Level pending

For $$A = (2^{334})!$$ and $$B = \displaystyle \prod_{n=0}^{100}(10^n)!$$

$$(A^{1000} - 1) / (A - 1) = P \times B + Q$$ where $$P$$ and $$Q$$ are non-negative integers and $$Q < B$$

$$Q = 1000000 \times R + S$$ where $$R$$ and $$S$$ are non-negative integers and $$S < 1000000$$

Find $$S$$

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