AMC 8 2014 Problem 13

If $n$ and $m$ are integers and $n^2+m^2$ is even, which of the following is impossible? $\textbf{(A) }$ $n$ and $m$ are even $\textbf{(B) }$ $n$ and $m$ are odd $\textbf{(C) }$ $n+m$ is even $\textbf{(D) }$ $n+m$ is odd $\textbf{(E) }$ none of these are impossible