F. Four in a Row
time limit per test
6 с
memory limit per test
512 megabytes
input
standard input
output
standard output

With a rush of people buying gifts for Valentine's Day, Magikarp is waiting in a line of $$$n$$$ people at KarpMart when he notices that out of the $$$n$$$ people in line, there are exactly $$$k$$$ subarrays of length 4 where the people are lined up in increasing height order. Magikarp now wonders: if these $$$n$$$ people were to rearrange themselves, how many total permutations would also have exactly $$$k$$$ length-4 subarrays with increasing height order. Print your answer in mod $$$10^9+7$$$.

Assume that all $$$n$$$ people have different heights.

Input

The first line of input contains 2 integers $$$n$$$ and $$$k$$$ $$$(4\le n\le 500, 0\le k\le n-3)$$$ — the number of people and the number of desired increasing length-4 subarrays.

Output

Output a single integer in mod $$$10^9+7$$$, the total number of permutations with exactly $$$k$$$ length-4 subarrays of increasing heights.

Examples
Input
5 1
Output
8
Input
20 6
Output
965696799
Note

In the first sample, there are 5 people. Suppose they have heights $$$1,2,3,4,5$$$. The 8 possible permutations are:

1 2 3 5 4

1 2 4 5 3

1 3 4 5 2

2 1 3 4 5

2 3 4 5 1

3 1 2 4 5

4 1 2 3 5

5 1 2 3 4