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