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Defining a power series with variable coefficients

It is not difficult to define a multivariate power series; for example, the following works:

R.<a,x,y> = PowerSeriesRing(ZZ,3)
f = a*x + y + x*y + O(a,x,y)^3

But what I would really like is to treat the series f as a series in x and y, with a acting as a variable coefficient, so that, for example, I could instead write f = a*x + y + x*y + O(x,y)^3. I tried the following:

M = PolynomialRing(ZZ,'a')
R.<x,y> = PowerSeriesRing(M,2)
f = a*x + y + x*y + O(x,y)^3

This generates the error "name a is not defined." What can I do to get a into the coefficient ring?