Idea for MVECTOR problem

[majidesmaili]

SPOJ.com - Problem MVECTOR

Im thinking for this a long time

My idea is:

Suppose the final SigmaX and SigmaY are both positive،
So we must collect all items which both x and y are positive and we must not collect any items which both x and y are negative, Then we have to collect some items which x*y<0

Im stuck on solving this. Plz give me a little hope.

[tjm]

Consider a simpler problem first, where we are also given a direction vector
and want to construct sum of vectors that goes as far as possible in that
specific direction.

Vectors that should be included in the sum are those that form an angle of at
most 90 degrees with direction vector, while those that form an angle above 90
should be omitted.

To generalize the solution of the problem, consider all possible directions
by performing an angular sweep.