General partial fraction decomposition for a specific type of rational function

Question

Given a rational function of the form $$ \frac{x^k}{(x^n-\lambda_1)(x^m-\lambda_2)}$$ with $k< n+m$, I know we can prove that there are unique polynomials $p(x),q(x)$ with $$ \frac{x^k}{(x^n-\lambda_1)(x^m-\lambda_2)} = \frac{p(x)}{x^n-\lambda_1}+\frac{q(x)}{x^m-\lambda_2} $$ where $\deg p(x) <n$, $\deg q(x)<1$, but is there a general formula for finding $p$ and $q$ in terms of $n,m,k,\lambda_1,\lambda_2$?