Binary XOR

You are given two binary strings $A$ and $B$, each with length $N$. You may reorder the characters of $A$ in an arbitrary way and reorder the characters of $B$ also in an arbitrary (not necessarily the same) way. Then, you should compute the XOR of the resulting strings. Find the number of distinct values of this XOR which can be obtained, modulo $1,000,000,007$ ($10^9 + 7$). ### Input - The f