CSES - Permutation Inversions
  • Time limit: 1.00 s
  • Memory limit: 512 MB
Your task is to count the number of permutations of $1,2,\dots,n$ that have exactly $k$ inversions (i.e., pairs of elements in the wrong order).

For example, when $n=4$ and $k=3$, there are $6$ such permutations:
  • $[1,4,3,2]$
  • $[2,3,4,1]$
  • $[2,4,1,3]$
  • $[3,1,4,2]$
  • $[3,2,1,4]$
  • $[4,1,2,3]$
Input

The only input line has two integers $n$ and $k$.

Output

Print the answer modulo $10^9+7$.

Constraints
  • $1 \le n \le 500$
  • $0 \le k \le \frac{n(n-1)}{2}$
Example

Input:
4 3

Output:
6