jmc

We can factor the given product using Simon's Favorite Factoring Trick. Factor $1001001$ out of the first two terms and $-1001$ out of the second two terms to find $$(1001001)(1010101+989899)-1001(989899+1010101).$$Since $1010101+989899=2000000$, we can complete the factoring as $$\begin{array}{rl}(1001001-1001)(2000000)& =(1000000)(2000000)\\ & =2000000000000.\end{array}$$Thus we can see that the rightmost non-zero digit $a=2$, and it is followed by 12 zeroes so $b=12$. Thus $(a,b)=\boxed{(2,12)}$.