Permutation $p$ is an ordered set of integers $p1$,$p2$,...,$pn$ consisting of $n$ distinct positive integers, each of them doesn’t exceed $n$. We will denote the $i^{th}$ element of permutation $p$ as $pi$. We will call number $n$ the size or the length of permutation $p1$,$p2$,...,$pn$.

We will call position $i$ (1 ≤ i ≤ n) in permutation $p1$,$p2$,...,$pn$ good, if $|p[i]-i|=1$.

Your task is to count the number of permutations of size $n$ with exactly $k$ good positions.

Give the answer for $n$=1000 and $k$=700 modulo $1000000007$.

Example :- for $n=3$ and $k=2$ answer will be $4$.

$(1,3,2), (3,1,2), (2,1,3), (2,3,1)$ all have exactly $2$ good position.