Let $a(n)$ be the number of permutations $\pi$ of length $n$ satisfying $\pi(y) = x$ if and only if $\pi(n - x + 1) = y$ for all $x$.

Find $\displaystyle \sum_{k=1}^{10^{6}}a(k)$ mod $10^9+7$

Example: $a(4) = 2$ and two permutations are : $2413, 3142$