Covariance of two functions

Question

We are given the following expression of a model: $$Y_t=b_0+b_1Y_{t-1}+u_t$$ $$K_t=a_0+a_1Y_{t-1}+w_t$$ These can be written in the alternative manner: $$Y_t= \frac{b_0}{1-b_1}+\sum_{j=0}^\infty b_{1}^j u_{t-j}$$ $$K_t= \frac{a_0}{1-a_1}+\sum_{j=0}^\infty a_{1}^j w_{t-j}$$ We are also given that $$E[Y_t]= \frac{b_0}{1-b_1}$$ $$Var(Y_t)= \frac{\sigma_u^2}{1-b_1^2}$$ and that $$E[K_t]= \frac{a_0}{1-a_1}$$ $$Var(K_t)= \frac{\sigma_w^2}{1-a_1^2}$$ How can we use the above results to calculate the covariance bellow? $$Cov(Y_t,K_t)= \frac{Cov(u,w)}{1-b_1a_1}$$