How to calculate the complex multivariate integral?

Consider the 2-fold countur integral, x,y are complex variables :

(2 \pi I)^{-2} * Integral_{|x|=1} Integral_{|y|=1} [(x^{a+m-1} y^{b
+n-1}/(x^a*y^b-1)] dx dy

From another considerations, the integral is equal to 1 if a=m,
b=n and 0 othewise, but I cant prove it by direct calculation.
Anybody can help?
.