You are given two integers $n$ and $m$. You are required to find the number of permutations of $n$ such that for each $i$ the $|a_i - i| ≠ m$ where $|x - y|$ denotes the absolute difference between $x$ and $y$.

Example:

Here, $n = 4$ and $m = 3$, therefore, the valid permutations are $[2\ 4\ 1\ 3]$, $[1\ 3\ 4\ 2]$, and so on. The invalid permutations for the same are $[4\ 1\ 3\ 2]$, $[3\ 2\ 4\ 1]$, and so on.

Note: As the number can be large, print answer modulo $1000000007$.

Input format

The first line contains two integers $n$ and $m$.

Output format

Print one integer denoting the number of permutations that are valid. As the number can be very large, print answer modulo $1000000007$.

Constraints

 $2 ≤ n ≤ 1e3\\ 1 ≤ m < n$