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 3\,000~

~0 \le K \le 3\,000~

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]~.