Given two integers n and k, find how many different arrays consist
of numbers from 1 to n such that there are exactly k
inverse pairs.
We define an inverse pair as following: For ith and
jth element in the array, if i < j and
a[i] > a[j] then it's an inverse pair; Otherwise, it's
not.
Since the answer may be very large, the answer should be modulo 109 + 7.
Example 1:
Input: n = 3, k = 0 Output: 1 Explanation: Only the array [1,2,3] which consists of numbers from 1 to 3 has exactly 0 inverse pair.
Example 2:
Input: n = 3, k = 1 Output: 2 Explanation: The array [1,3,2] and [2,1,3] have exactly 1 inverse pair.
Note:
n is in the range [1, 1000] and k is in the range
[0, 1000].