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$\color{#D61F06}{A}$ and $\color{#3D99F6}{B}$ are whole numbers that do not contain 0 as a digit when expressed in base 10

If $\color{#D61F06}{A} \times \color{#3D99F6}{B} = 10000,$ then what is $\color{#D61F06}{A}+\color{#3D99F6}{B}?$

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