PI operator with two variables

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$$\prod_{\begin{array}{c}b=1,\cdots,B \\ d=1,\cdots,D\end{array}}e^{-\lambda(b,d)}\,\frac{\lambda(b,d)^{n(b,d)}}{n(b,d)!}. $$

In the above expression, what does the PI operator stand for with two variables?

Can I think that is dual PI operators such as

$$ \prod_{d=0}^{D}\prod_{b=0}^{B} $$

Thank you for considering my request.