Hochschild cohomology of the algebra of conformal endomorphisms

We prove that all Hochschild cohomology groups of the associative conformal algebra of conformal endomorphisms $\mathrm{Cend}_k$ with coefficients in an arbitrary conformal bimodule $M$ are trivial starting from the dimension 2, i.e., $H^n(\mathrm{Cend}_k, M) = 0$ for $n\ge 2$.