Due to boredom, Barr the bear is entertaining himself with N miniature bear figures! And unsurprisingly, these little bears are labelled from 1 to N. Barr wants to line them up in a row. However, Barr imposes strict lining regulations.
We call a pair of bears labelled i and j an awesome pair if i is before j in the line and i > j. The awesomeness of the lineup is the number of awesome pairs in it. For example, the awesomeness of the lineup (1, 4, 3, 2) is 3 because there are 3 awesome pairs: (4, 3), (4, 2) and (3, 2).
Barr wants the awesomeness of the lineup to be exactly C, as he deems it optimal. If the lineup is not awesome enough, he will be sad. If the lineup is too awesome, he will be very sad. Help Barr remain happy by determining the number of such lineups! As the number can be very big, output it modulo 1,000,000,007.
The first and only line of input contains two integers, N
(1 ≤ N
≤ 1,000) and C
(0 ≤ C
Output the number of lineups modulo 1,000,000,007.
Sample Input 1
Sample Output 1
Sample Input 2
Sample Output 2
Sample Input 3
Sample Output 3