[Tex/LaTex] Overrunning superscript in product written in “Pi notation”

Question

How do you deal with the problem of an overrunning superscript in a product written in Pi notation? E.g.

In this case it seems that the extra space before and after the Pi is unnecessary, so maybe it could be omitted?

Another solution I guess is naming the expression using a variable and use the variable name as the superscript.

\documentclass{article}
\begin{document}
\[
  N_A!\prod_{k=1}^{(N_A-N_B)/2} (2k - 1)
\]
\end{document}

Answer 1

Not sure it looks better, but to answer the direct question, the space of the superscript can be ignored with \mathclap of the mathtools package.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
  N_A!\prod_{k=1}^{\mathclap{(N_A-N_B)/2}} (2k - 1)
\]
\end{document}