# Switch, switch, switch

Logic Level 3

Let $$A$$ and $$B$$ are 2-digit positive integers, where $$A>B$$ and $$A+B=100$$.

If we switch the digits in $$B$$ (call it $$B'$$), $$B'$$ will be the product of both digits of $$A$$.

If we switch the digits in $$A$$ (call it $$A'$$), the absolute difference between the new $$A'$$ and $$B$$ will equal to $$B' + 1$$.

Find $$A \times B$$.

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