MathDB

n

students take a test with

m

questions, where

m,n\ge 2

are integers. The score given to every question is as such: for a certain question, if

x

students fails to answer it correctly, then those who answer it correctly scores

x

points, while those who answer it wrongly scores

0

. The score of a student is the sum of his scores for the

m

questions. Arrange the scores in descending order

p_1\ge p_2\ge \ldots \ge p_n

. Find the maximum value of

p_1+p_n

Problem Statement