Permutation Inversions

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