Školjka

%V0 In the coordinate plane consider the set $S$ of all points with integer coordinates. For a positive integer $k$, two distinct points $a$, $B\in S$ will be called $k$-friends if there is a point $C\in S$ such that the area of the triangle $ABC$ is equal to $k$. A set $T\subset S$ will be called $k$-clique if every two points in $T$ are $k$-friends. Find the least positive integer $k$ for which there exits a $k$-clique with more than 200 elements. Proposed by Jorge Tipe, Peru