Abbreviating the Product of a Range

Compute the product of all integers in [left, right] and return its abbreviated form " ...<suf>eC" where C is the count of trailing zeros removed and /<suf> are the first/last five digits of the product after removing zeros (or the full number if ≤10 digits). The algorithmic challenge is to determine the leading five digits and the trailing five nonzero digits efficiently for ranges up to 10^4 without constructing the full huge product (typically via logarithms for the prefix and modular arithmetic with factor cancellation for the suffix).