Problem Description

Given a permutation of length $n$, find the number of permutations whose number of inversions is exactly $c$. Output the result modulo $10^9+7$.

Input Format

The input consists of one line with two integers $n, c$.

Output Format

Output the number of permutations whose number of inversions is exactly $c$. Output the result modulo $10^9+7$.

10 1

9

4 3

6

9 13

17957

Hint

Constraints

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

Notes

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

Translated by ChatGPT 5