Inverse of a Function

The *beauty* of a sequence of non-negative integers is computed in the following way: for each of its non-empty (not necessarily contiguous) subsequences, compute the XOR of all elements of this subsequence; then, sum up all the XORs you obtained. Let $F(N, B)$ denotes the number of non-negative integer sequences with length $N$ which have beauty $B$. You are given three integers $N$, $X$ and $