Cohomology of K(1) acting on the superspace of bilinear differential operators

We consider the 1|1-dimensional real superspace R-1|1 endowed with its standard contact structure defined by the 1-form alpha. The conformal Lie superalgebra K(1) acts on R-1|1 as the Lie superalgebra of contact vector fields. We compute the first differential cohomology of K(1) with coefficients in superspace D-lambda,D-mu;nu of bilinear differential operators acting on weighted densities. This work is the simplest super analog of the problems solved in Ref. 5.