Question

Suppose p(x,y|a)=p(T(x),y|a)h(x,y) and p(x,a)=p(T(x)|a)g(x), where a is the parameter of inference and T(x) is a sufficient statistic for a.

Then, g(x)= {int p(T(x),y|a)h(x,y)}/ {int p(T(x),y|a)}, (int means integral over y), then is it true that h(x,y) is only a function of x? If not, can you give the counterexample? Thanks.