Let the selected interval be {A,...,A+R-1}. Define f(z)=(-1)^A*sum_{j=0}^{R-1}(-2)^j*binom(z-A,j), where binom(z-A,j)=(z-A)(z-A-1)...(z-A-j+1)/j!, and the j=0 product is one. This is a rational polynomial of degree at most R-1. At z=A+m for 0<=m<R, terms j>m vanish and the binomial theorem gives f(A+m)=(-1)^A*(1-2)^m=(-1)^(A+m). The swap matrix is M_0=V*f(W). This explicit choice matters for bounding coefficient denominators; existence of an interpolating polynomial alone does not provide those bounds.