String of templated struct at compile time

[divi]

Due to prior design choices, I have the following setup:

enum K { A, B }

mixin template Magic()
{
   mixin(`alias Other = ` ~ magic() ~ `!(K.B);`);
}

struct S(K k) if (k == K.B) {}
struct S(K k)
   if (k == K.A)
{
   mixin Magic; // magic() returns "S"
}

struct T(K k) if (k == K.B) {}
struct T(K k)
   if (k == K.A)
{
   mixin Magic; // magic() returns "T"
}

alias A(alias T) = T!(K.A);

void main()
{
   A!S a;
}


Is there any possible way I can write magic() so that the above 
code works as intended? n.b. it must be able to go through the 
alias A.

For what it's worth, I'm trying to define "Other" for the generic 
struct parameterised with k == K.A such that I can instantiate 
it's sister struct parameterised by K.B, e.g.

A!S a; // type is S!(K.A)
alias U = a.Other;
U b; // type is S!(K.B)