Let be integers such that Determine the maximum size of a subset of the set such that no distinct elements of add up to
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Let $k,m,n$ be integers such that $1 < n \leq m - 1 \leq k.$ Determine the maximum size of a subset $S$ of the set $\{1,2,3, \ldots, k-1,k\}$ such that no $n$ distinct elements of $S$ add up to $m.$
Source: Međunarodna matematička olimpijada, shortlist 1996
Školjka 
be integers such that 
Determine the maximum size of a subset 
of the set 
such that no 
distinct elements of 