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Let

m \ge n

be positive integers. Frieder is given

mn

posters of Linus with different integer dimensions of

k \times l

with

1 \ge k \ge m

and

1 \ge l \ge n

. He must put them all up one by one on his bedroom wall without rotating them. Every time he puts up a poster, he can either put it on an empty spot on the wall or on a spot where it entirely covers a single visible poster and does not overlap any other visible poster. Determine the minimal area of the wall that will be covered by posters.

7

Problems(1)