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{align*}(1001001-1001)(2000000)&=(1000000)(2000000)\\&=2000000000000.\end{align*}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)} $.