I have a list and need to remove certain members of the list.

lis = {f1,a,b,c,d,f2,e,g,h,i,f1,j,k,l,m,f2,n,o}

I need to remove each occurrence of f1 and the following two elements, and remove each occurrence of f2 and the following element. (f1 and f2 will always at least two elements apart). This gives:

res = {c,d,g,h,i,l,m,o}

ReplaceList would seem to be useful, but I am not able to see it. Thanks for any suggestions.