Morita equivalence of $K$-algebras

Given $K$ a unital commutative ring and $A$ a $K$-algebra different from $K$. Can $K$ be Morita equivalent to $A \amalg A$, where $A \amalg A$ is the coproduct in the category of unital associative $K$-algebras?

If V is a vector space such that $$V\oplus V$$ is isomorphic to V then A=TV, the tensor álgebra, is isomorphic to $$T(V\oplus V)=A\coprod A$$, in particular Morita equivalent