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