This paper presents some new protocols for (M+1)st-price auction, a style of auction in which the highest M bidders win and pay a uniform price, determined by the (M+1)st price. A set of distributed servers collaborates to resolve the (M+1)st price without revealing any information in terms of bids including the winners' bids. A new trick to jointly and securely compute the highest value as a degree of distributed polynomials is introduced. The building block requires just one round for bidders to cast bids and one round for auctioneers to determine the winners.