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Algebra Level 3

m=442(m212)(m222)m2(m232)\prod_{m=4}^{4^2} \dfrac{\big(m^2-1^2\big)\big(m^2-2^2\big)}{m^2\big(m^2-3^2\big)}

If the value of the product above is equal to AB\frac AB, where AA and BB are coprime positive integers, find ABA-B.

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