KGS math club/solution 11 2

Given n, k, and a k-member subset K of the n-member set N, we form the (n-k)-member subset it is paired with as follows.

Assign integers modulo n to the members of N, and cyclically order its members using them. Remove from N a member of K with a non-member of K that immediately follows it; and repeat until there are no members of K left. Append what we have left to K.