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.
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 a single integer in mod $$$10^9+7$$$, the total number of permutations with exactly $$$k$$$ length-4 subarrays of increasing heights.
5 1
8
20 6
965696799
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
