Every two of $200$ points in space are connected by a segment, no two intersecting each other. Each segment is painted in one colour, and the total number of colours is $k$. Peter wants to paint each of the $200$ points in one of the colours used to paint the segments, so that no segment connects two points both in the same colour as the segment itself. Can Peter always do this if (a) k = 7; (4 points) (b) k = 10? (4 points)