KöMaL 2005 A384

$a_0$,$a_1$,...,$a_n$ and $b_0$,$b_1$,...,$b_k$ are non-negative real numbers, such that $a_0$=$b_0$=1 and ($a_0$+$a_1 x$+...+$a_n x^n$)($b_0$+$b_1 x$+...+$b_k x^k$)=1+$x$+...+$x^{n+k}$. Prove that each of the numbers $a_i$ and $b_i$ is either 0 or 1.