Equal Hamming Distance

Chef is given two binary strings $A$ and $B$, each having length $N$. Chef wants to find the number of binary strings $C$, of length $N$, such that $H(A, C) = H(B, C)$, where $H(X, Y)$ denotes the *hamming distance* between the strings $X$ and $Y$. Since the answer can be large, output it modulo $10^9+7$. Note: [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) between two strin