  In a recent paper, Stasinski and Voll introduced a length-like statistic on
hyperoctahedral groups and conjectured a product formula for this statistic's
signed distribution over arbitrary quotients. Stasinski and Voll proved this
conjecture for a few special types of quotients. We prove this conjecture in
full, showing it holds for all quotients. In the case of signed permutations
with at most one descent, this formula gives the Poincare polynomials for the
varieties of symmetric matrices of a fixed rank.
