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 i_{th}
and j_{th}
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 10^{9} + 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].Subscribe to see which companies asked this question.