Calculate the number of permutations of the first $N$ positive integers which can be sorted by performing exactly $K$ swaps of adjacent elements.

Constraints

$2\le N\le 3000$

$0\le K\le 3000$

Input Specification

The only line contains two space-separated integers, $N$ and $K$.

Output Specification

Output the number of permutations of the first $N$ positive integers which can be sorted by performing exactly $K$ adjacent swaps. Since this value may be large, output it modulo ${10}^9+7$.

Sample Input

3 3

Sample Output

3

Explanation for Sample

The permutations of $[1,2,3]$ which can be sorted by performing exactly $3$ adjacent swaps are $[2,1,3]$, $[1,3,2]$ and $[3,2,1]$.