Let `a=3^(1/223) +1` and for all `n ge 3` let `f(n) = C(n,0) a^(n-1) - C(n,1).a^(n-2) -C(n,2) a^(n-3) -...+(-1)^(n-1).C(n,n-1)` If the value of `f(2007) +f(2008) =3^k` where `k in N` then the value of k is