Problem Description

Find the number of permutations of length $n$ that have exactly $c$ inversions, modulo $10^9+7$.

Input Format

The input consists of a single line containing two integers $n$ and $c$.

Output Format

Output the number of permutations with exactly $c$ inversions, modulo $10^9+7$.

Sample Input and Output

Sample Input #1

10 1

Sample Output #1

9

Sample Input #2

4 3

Sample Output #2

6

Sample Input #3

9 13

Sample Output #3

17957

Notes

Data Size and Constraints

For $100\%$ of the data, it is guaranteed that $1 \le n \le 10^3$ and $1 \le c \le 10^4$.

Note

This problem is translated from COCI2006-2007 CONTEST #4 T4 ZBRKA

见题面 Input 部分

见题面 Output 部分