Two moles of an ester (A) are condensed in the presence of sodium ethoxide to give a `beta`-keto-ester (B) and ethanol. On heating in an acidic solution, (B) gives ethanol and `beta`-keto acid (C). On decarboxylation, (C) gives 3-pentanone. Identify (A), (B) and (C) with proper reasoning. Name the reaction involved m the conversion of (A) to (B).